Mapping and quantifying shear stress and hemolysis in patients having LVADS

ABSTRACT

Provided herein are methods for in-vivo assessment of intraventricular flow shear stress, risk of hemolysis, also the location and extent of blood flow stasis regions and inside a cardiac chamber or blood vessel. Also provided herein are systems for performing such methods. Also provided herein are methods for assessing hemolysis and/or thrombosis risk in patients implanted with an LVAD. LVAD positioning and/or speed may be adjusted based on the results obtained by using methods described herein, and the risk for hemolysis and/or thrombosis can be minimized.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a National Stage Application under 35 U.S.C. § 371and claims the benefit of International Application No.PCT/US2019/026146, filed Apr. 5, 2019, which claims priority to U.S.Provisional Application Ser. No. 62/653,365 and U.S. ProvisionalApplication Ser. No. 62/653,389, both filed on Apr. 5, 2018, thedisclosures of which are herein incorporated by reference in theirentireties.

FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under Grant No. 1R21HL108268-01 awarded by the National Institutes of Health. The Governmenthas certain rights in the invention.

TECHNICAL FIELD

Provided herein are methods for determining the presence of intracardiacthrombosis and/or hemolysis, or risks of thrombosis and/or hemolysis, ina patient (e.g., a patient having a LVAD) by assessing the location andextent of intraventricular blood dynamics inside a cardiac chamber.

BACKGROUND

Cardiovascular diseases are the leading cause of mortality worldwide andare projected to cause more than 20 million deaths per year by 2030.Cardiogenic shock remains the main cause of mortality in patientshospitalized for an acute myocardial infarction despite earlyrevascularization (1). In this scenario, short-term mechanicalcirculatory support provides a crucial time span for the recovery of thestunned myocardium (2). Although the mortality of these patients is ashigh as 40% (3-5), hospital survivors have an excellent chance forlong-term survival. Therefore, any improvement in short-term outcomesentails huge clinical impact.

In patients with advanced heart failure, refractory to medical therapy,treatment with left ventricular assist devices (LVADs) decreasesmortality and improves quality of life. Therefore, these devices areincreasingly being used, both as bridge therapy to cardiactransplantation and as destination therapy. Currently, there are a lackof clinical tools to guide optimal LVAD settings and cannula placementto improve outcomes and decrease complications. Ramp studies withstandard echocardiographic views are sometimes used to choose pumpspeeds, but there are limited data showing the utility of this approach.Two important complications of LVAD therapy are hemolysis andthrombosis. Hemolysis is known to be associated with regions of highshear stress and thrombosis is associated with relative stasis, butcurrently the risks of these are difficult to estimate in clinicalpractice and therefore difficult to mitigate. Understanding the effectsof an LVAD on intraventricular flow patterns and hemodynamics may helpguide optimal pump settings, provide input on optimum cannula placement,decrease the rate of complications, and improve outcomes.

The normal LV flow pattern consists of a large diastolic vortex thatchannels the transit of blood towards the aortic valve. This vortexcontributes to diastolic suction and minimizes kinetic energy losses andcardiac work (6, 7). In patients with LV systolic dysfunction, abnormalvortex structures are associated with greater energy dissipation anddecreased pumping efficiency. These flow patterns drive complex fluidtransport processes, whose impact on cardiovascular physiology anddisease remains unexplored, especially in patients implanted with assistdevices. Blood particles follow convoluted trajectories inside the LV(8-10). Intraventricular stasis and hemodynamic stresses are thecumulative result of the dynamical interactions between incoming flowand residual flow from preceding cycles (11). In the healthy heart, as aresult of these processes there are minimal associated blood stasis andshear-induced hemolysis. However, intraventricular flow patterns can besignificantly altered in cardiomyopathies (12-15), leading to increasedblood stasis (14, 16). It has recently been shown that intraventricularcannula implantation and flow suction can also significantly alter theseflow patterns in LVAD-implanted patients (17, 18). Likewise,biventricular pacemaker settings affect the efficiency of LV bloodredirection (19).

Thus, it has been recognized that a deeper understanding of LV bloodflow dynamics in normal and diseased LVs, may enhance the currentcharacterization of cardiac physiology and lead to a better knowledge ofthe pathophysiology of HF, facilitate subclinical diagnosis of cardiacdiseases, improve tools used for characterizing, predict risk ofthrombus formation and guide treatment strategies. With the use of thecurrent generation of continuous-flow assistances, the natural bloodflow path through the heart is necessarily disrupted to some degree.Proper positioning and speed adjustment of these devices provide anoptimal flow and minimize hemolysis related to shear stress blood damage(17, 20). Also, the decrease of the natural flow pulsatilityaccompanying continuous flow support may exacerbate the mixing of blood,decreasing intraventricular washout and potentially increasingcardioembolic risk.

SUMMARY

In some embodiments, novel echocardiographic modalities to map bloodflow velocity inside the LV and its changes during the cardiac cycle areprovided herein. In some embodiments, novel echocardiographic modalitiesprovided herein include 2D echo color Doppler velocimetry (echo-CDV). Insome embodiments, novel echocardiographic modalities provided hereinallow for non-invasive personalized risk assessment of hemolysis andblood clot formation inside the left ventricle.

In some embodiments, obtaining flow-velocity images of blood inside acardiac chamber or blood vessel (e.g. a cardiac chamber or blood vesselin a subject having a LVAD) is performed using a medical image-basedapparatus able to determine blood flow velocity field. For example, themedical image-based apparatus can be an echocardiogram apparatus, amagnetic resonance imaging (MRI) apparatus, an echocardiographic imagingapparatus, a 2D color-Doppler velocimetry (echo-CDV) apparatus, anecho-particle-image-velocimetry (echo-PIV) apparatus, a syntheticaperture ultrasound apparatus or a transverse oscillation ultrasoundvector velocimetry apparatus, or other medical image-based apparatusknown to the skilled artisan. In some embodiments, flow-velocity imagesobtained from the medical image-based apparatus and suitable for themethods described herein include one, two, or three-dimensional imagesresolved in time.

In some aspects, provided herein are methods for characterizing vortexpatterns inside a cardiac chamber or blood vessel of a subject (e.g., asubject having a LVAD) comprising obtaining flow-velocity images ofblood inside a cardiac chamber or blood vessel of a subject, calculatingthe flow vorticity, ω, which will be used to characterize the flowstructures by tracking flow patterns in time. The flow structures can becharacterized by their circulation, kinetic energy, radius, aspectratio, and the trajectory of their center.

In some aspects, provided herein are methods for assessing the risk ofcumulative blood shear stress and hemolysis comprising calculating theplasma free hemoglobin, total hemoglobin the blood, cumulative fluidshear stress, and residence time (TR) (e.g., in a subject having aLVAD). The region of highest cumulative shear corresponds with theboundary of the LV vortex.

In some aspects, provided herein are methods for identifying regions ofblood flow stasis inside a cardiac chamber or blood vessel of a subject(e.g., a subject having a LVAD) comprising obtaining flow-velocityimages of blood inside a cardiac chamber or blood vessel of the subject,calculating the residence time (TR), the standard deviation of theresidence time (σ_R), kinetic energy, and/or rate of distortion of bloodparticles inside the cardiac chamber or blood vessel using theflow-velocity images to generate numerical metrics of blood flow, andgenerating residence time (TR), kinetic energy, and/or rate ofdistortion maps using the numerical metrics to identify and characterizeregions of blood flow stasis. Further, the disclosure provides a methodto systematically analyze the effect of LVAD support on LV fillingtransport where low K (kinetic energy) or/and high Ts are indicators ofblood stasis.

The cardiac chamber or blood vessel can be any cardiac chamber or bloodvessel in which the blood velocity can be resolved. For example, thecardiac chamber can be the left ventricular chamber, left atriumchamber, left atrial appendage, right-ventricular chamber, or rightatrium chamber. In some embodiments, regions of blood flow stasis aredetermined by calculating the residence time (TR), the standarddeviation of the residence time (σ_R), kinetic energy, and/or rate ofdistortion of blood particles in more than one cardiac chamber or bloodvessel (e.g., 2, 3, 4, 5, or more cardiac chambers or blood vessels).

In some embodiments, calculating the residence time (TR) of bloodparticles includes utilizing the equation:(∂_(t) T _(R))/∂_(t)+∇·({right arrow over (v)}T _(R))=1

In some embodiments, the disclosure provides methods to calculatepressure maps from flow velocity data from medical images.

In some embodiments, in patients with LVADs, the numerical metrics ofblood flow are additionally used to map the size and/or location ofblood transport structures that transit from and/or into device flowelements such as inflow and/or outflow cannulas. The normalizedorientation of the cannula may be used to parameterize cannulapositioning. The orientation of the cannula with respect to flowstructures may be a relevant parameter that dictates shear stresses,residence time, etc.

In some embodiments, provided herein are methods for identifying aregion of hemolysis inside a cardiac chamber or blood vessel of asubject having a LVAD that include: obtaining flow-velocity images ofblood inside a cardiac chamber or blood vessel of the subject;calculating hemolysis using the flow-velocity images using the followingequation:

$\frac{\Delta\;{PfHb}}{Hb} = {C\;\Sigma^{a}T_{R}^{b - 1}}$

wherein PfHb is the plasma free hemoglobin, Hb is the total hemoglobinin the blood (intracellular and extracellular), Σ is the cumulativefluid shear stress experienced by blood particles in seconds-1, TR isthe residence time of the blood particles in seconds, and a, b, and care empirical constants; wherein Σ is determined using the forcedtransport equation:

${\frac{D\;\Sigma}{Dt} = {{{\partial_{t}\Sigma} + {\nabla{\cdot \left( {v\;\Sigma} \right)}}} = S}},{{\Sigma\left( {x,{t = 0}} \right)} = 0},{{.{\Sigma\left( {x_{inlet},t} \right)}} = 0},$

wherein S is the Von-Mises stress at each point of space and time insidethe left ventricle, and wherein S is determined from a velocity fieldobtained from the flow velocity images.

In some embodiments, provided herein are methods for evaluating anintraventricular region of hemolysis inside a cardiac chamber or bloodvessel of a first subject that include: implanting a left ventricularassist device (LVAD) into the first subject at a first location, whereinthe LVAD operates under a first set of operating parameters; obtainingflow-velocity images of blood inside a cardiac chamber or blood vesselof the first subject; calculating hemolysis using the flow-velocityimages using the following equation:

$\frac{\Delta\;{PfHb}}{Hb} = {C\;\Sigma^{a}T_{R}^{b - 1}}$

wherein PfHb is the plasma free hemoglobin, Hb is the total hemoglobinin the blood (intracellular and extracellular), Σ is the cumulativefluid shear stress experienced by blood particles in seconds-1, TR isthe residence time of the blood particles in seconds, and a, b, and care empirical constants; wherein Σ is determined using the forcedtransport equation:

${\frac{D\sum}{Dt} = {{\partial_{t}{\sum{{+ \nabla} \cdot \left( {v\sum} \right)}}} = S}},{{\sum\left( {x,{t = 0}} \right)} = 0},{\quad{{{\sum\left( {x_{inlet},t} \right)} = 0},}}$

wherein S is the Von-Mises stress at each point of space and time insidethe left ventricle, and wherein S is determined from a velocity fieldobtained from the flow-velocity images.

In some embodiments, methods provided herein include calculating one ormore of residence time (TR), standard deviation of residence time (σTR),inside the cardiac chamber or blood vessel using the flow-velocityimages to generate numerical metrics of blood flow; and calculating oneor more of cumulative von-Mises stress map (Σ), standard deviation ofresidence von-Mises stress (σΣ), inside the cardiac chamber or bloodvessel using the flow velocity images to generate numerical metrics ofblood flow; or combinations thereof, using the numerical metrics toidentify and characterize regions of hemolysis. In some embodiments,generating numerical metrics of blood flow comprises calculating theplasma free hemoglobin (PfHb) inside the cardiac chamber or bloodvessel, and the standard deviation of plasma free hemoglobin (σPfHb). Insome embodiments, calculating the standard deviation of plasma freehemoglobin (σPfHb) in regions with high blood plasma free hemoglobin(PfHb) inside the cardiac chamber or blood vessel. In some embodiments,generating numerical metrics of blood flow comprises calculating therate of distortion of blood flow inside any cardiac chamber or bloodvessel. In some embodiments, calculating the blood flow's rate ofdistortion in regions with high blood plasma free hemoglobin (PfHb)inside the cardiac chamber or blood vessel. In some embodiments,generating numerical metrics of blood flow comprises calculating thesize, shape, mobility, distance to the chamber wall, and perimeter incontact with the chamber wall of regions with high blood plasma freehemoglobin (PfHb).

In some embodiments, the cardiac chamber is any cardiac chamber or bloodvessel in which the blood velocity can be resolved. In some embodiments,the cardiac chamber is the left ventricular chamber, left atriumchamber, left atrial appendage, right-ventricular chamber, or rightatrium chamber.

In some embodiments, obtaining flow-velocity images of blood inside acardiac chamber or blood vessel is performed using a medical image basedapparatus able to determine blood flow velocity field. In someembodiments, the medical image-based apparatus is an echocardiogramapparatus, a magnetic resonance imaging (MRI) apparatus, anechocardiographic imaging apparatus, a 2D color-Doppler velocimetry(echo-CDV) apparatus, an echo-PIV apparatus, a synthetic apertureultrasound apparatus, or a transverse oscillation ultrasound vectorvelocimetry apparatus. In some embodiments, the flow-velocity imagescomprise one, two, or three-dimensional images resolved in time. In someembodiments, multiple flow-velocity images are obtained using differentvelocity scales, and wherein data from the obtained flow velocity imagesare retrospectively merged to generate a flow map, a residence time (TR)map, a cumulative von-Mises stress map (Σ), a rate of distortion map, orcombinations thereof. In some embodiments, calculating the residencetime (TR) of blood particles comprises utilizing the equation:

${\frac{\partial T_{R}}{\partial t} + {\nabla{\cdot \left( {\overset{\rightarrow}{v}T_{R}} \right)}}} = 1.$

In some embodiments, the standard deviation of Σ is caused by noise inthe velocity measurements, and wherein calculating the standarddeviation of Σ comprises utilizing the equation:σ_(Σ)(x,t)=√{square root over (S _(Σ)(x,t)−Σ²(x,t))}

wherein SΣ and Σ obey the equations:

${\frac{\partial\sum}{\partial t} + {\nabla{\cdot \left( {\overset{\rightarrow}{v}\sum} \right)}}} = {S + {\nabla{\cdot \left( {k{\nabla\sum}} \right)}}}$${{\frac{\partial S_{\sum}}{\partial t} + {\nabla{\cdot \left( {\overset{\rightarrow}{v}S_{\sum}} \right)}}} = {2{\sum{{+ \nabla} \cdot \left( {k{\nabla S_{\sum}}} \right)}}}},$

and wherein diffusivity coefficient k represents uncertainty introducedby the noise in the velocity measurements.

In some embodiments, the standard deviation of TR is caused by noise inthe velocity measurements, and wherein calculating the standarddeviation of TR comprises utilizing the equation:σ_(TR)(x,t)=√{square root over (S _(R)(x,t)−T _(R) ²(x,t))}

wherein SR and TR obey the equations:

${\sigma_{TR}\left( {x,t} \right)} = \sqrt{{S_{R}\left( {x,t} \right)} - {T_{R}^{2}\left( {x,t} \right)}}$${{\frac{\partial S_{R}}{\partial t} + {\nabla{\cdot \left( {\overset{\rightarrow}{v}S_{R}} \right)}}} = {{2T_{R}} + {\nabla{\cdot \left( {k{\nabla S_{R}}} \right)}}}},$

and wherein diffusivity coefficient k represents uncertainty introducedby the noise in the velocity measurements.

In some embodiments, a distribution of values of cumulative von-Misesstress at each instant of time and each point in space, whichdistribution of values of cumulative von-Mises stress is caused by noisein the velocity measurements, wherein a probability density function ofdistribution p(Σ, x, t) is calculated utilizing the equation:

$\frac{\partial p}{\partial t} = {{- \frac{\partial({vp})}{\partial x}} - \frac{\partial p}{\partial T} + {\frac{\partial}{\partial x}{\left( {k\frac{\partial p}{\partial x}} \right).}}}$

and wherein diffusivity coefficient k represents uncertainty introducedby the noise in the velocity measurements.

In some embodiments, a distribution of values of residence time emergesat each instant of time and each point in space, which distribution ofvalues of residence time is caused by noise in the velocitymeasurements, wherein a probability density function of distributionp(T, x, t) is calculated utilizing the equation:

$\frac{\partial p}{\partial t} = {{- \frac{\partial({vp})}{\partial x}} - \frac{\partial({Sp})}{\partial S} + {\frac{\partial}{\partial x}{\left( {k\frac{\partial p}{\partial x}} \right).}}}$

and wherein diffusivity coefficient k represents uncertainty introducedby the noise in the velocity measurements.

In some embodiments, numerical metrics of blood flow are used toidentify size, location, or both, of high blood plasma free hemoglobin(PfHb) within the cardiac chamber or blood vessel.

In some embodiments, a LVAD is surgically implanted into the subject. Insome embodiments, LVAD is temporarily implanted into the subject. Insome embodiments, the LVAD is a catheter-based LVAD.

In some embodiments, methods provided herein include evaluating anintraventricular region of hemolysis inside a cardiac chamber or bloodvessel of a second subject comprising: implanting a LVAD into the secondsubject at a second location, wherein the LVAD operates under a secondset of operating parameters; obtaining flow-velocity images of bloodinside a cardiac chamber or blood vessel of the first subject;calculating hemolysis using the flow-velocity images using the followingequation:

$\frac{\Delta\;{PfHb}}{Hb} = {C{\sum^{a}T_{R}^{b - 1}}}$

wherein PfHb is the plasma free hemoglobin, Hb is the total hemoglobinin the blood (intracellular and extracellular), Σ is the cumulativefluid shear stress experienced by blood particles in seconds-1, TR isthe residence time of the blood particles in seconds, and a, b, and care empirical constants; wherein Σ is determined using the forcedtransport equation:

${\frac{D\sum}{Dt} = {{\partial_{t}{\sum{{+ \nabla} \cdot \left( {v\sum} \right)}}} = S}},{{\sum\left( {x,{t = 0}} \right)} = 0},{\quad{{{\sum\left( {x_{inlet},t} \right)} = 0},}}$

wherein S is the Von-Mises stress at each point of space and time insidethe left ventricle, and wherein S is determined from a velocity fieldobtained from the flow-velocity images. In some embodiments, the firstlocation, the second location, or both is the location of cannulaplacement. In some embodiments, the first set of operating parameters,the second set of operating parameters, or both includes pump speed. Insome embodiments, the cardiac chamber of the second subject is the leftventricular chamber.

In some embodiment of methods provided herein, the subject, the firstsubject, or the second subject is a mammal. In some embodiments, themammal is a human. In some embodiments, the mammal is selected from thegroup consisting of: a monkey, a dog, a cat, a cow, a horse, a pig, arat, and a mouse.

The section headings used herein are for organizational purposes onlyand are not to be construed as limiting the described subject matter inany way. When definitions of terms in incorporated references appear todiffer from the definitions provided in the present teachings, thedefinition provided in the present teachings shall control. It will beappreciated that there is an implied “about” prior to metrics such astemperatures, concentrations, and times discussed in the presentteachings, such that slight and insubstantial deviations are within thescope of the present teachings herein. In this application, the use ofthe singular includes the plural unless specifically stated otherwise.Also, the use of “comprise,” “comprises,” “comprising,” “contain,”“contains,” “containing,” “include,” “includes,” and “including” are notintended to be limiting. It is to be understood that both the foregoinggeneral description and the following detailed description are exemplaryand explanatory only and are not restrictive of the invention. Thearticles “a” and “an” are used herein to refer to one or to more thanone (i.e., to at least one) of the grammatical object of the article. Byway of example, “an element” means one element or more than one element.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. Methods and materials aredescribed herein for use in the present invention; other, suitablemethods and materials known in the art can also be used. The materials,methods, and examples are illustrative only and not intended to belimiting. All publications, patent applications, patents, sequences,database entries, and other references mentioned herein are incorporatedby reference in their entirety. In case of conflict, the presentspecification, including definitions, will control.

The details of one or more embodiments of the invention are set forth inthe accompanying drawings and the description below. Other features,objects, and advantages of the invention will be apparent from thedescription and drawings, and from the claims.

DESCRIPTION OF DRAWINGS

This application contains at least one drawing executed in color. Copiesof this patent or patent application publication with color drawing(s)will be provided by the Office upon request and payment of the necessaryfee.

FIG. 1 displays head-to-head comparison of 2D echo-CDV and PCMRI bycomparing flow maps and vortex stats. Panel A shows flow maps obtainedby echo-CDV (left column) and phase-contrast MRI (right column) in apatient with dilated cardiomyopathy. The distributions of flow velocityand instantaneous streamlines are overlaid on anatomical images where,for echo-CDV, the LV wall is colored according to the values oflongitudinal myocardial strain and the identified vortex structures areoverlaid as yellow and cyan circles for the PCMRI and ultrasoundmethods, respectively. Panel B shows LV vortex circulation (top) andposition (bottom) along the cardiac cycle, as measured by ultrasound(blue lines) and PCMRI (red squares) in the same patient.

FIG. 2 displays a snapshot of cumulative blood shear at isovolumiccontraction in a patient with LV dysfunction mapping, based on echo-CDV.

FIG. 3 displays examples of blood transport analysis based on echo-CDV.Panel A shows tracking of the volumes of blood that enter the LV duringthe E wave, shown in gold, and A wave, shown in red, in a human LV.Panel B shows segmentation of LV blood volumes in the same LV at aorticvalve opening, showing direct flow (DF, green), retained inflow (RI,yellow), delayed ejection (DE, blue) and residual volume (RV, red).

FIG. 4 displays a snapshot of blood stasis indices at isovolumiccontraction in a patient with LV dysfunction. Panel A showsintraventricular residence time TR and instantaneous streamlines, PanelB shows Kinetic Energy Density (K) in the two residual volumes with TR>2sec, and Panel C shows Distortion time (TS) in the same residualvolumes.

FIG. 5 displays Echo 2D velocity fields and hemodynamic pressure maps.Each panel represents a different instant of the cardiac cycle, where1st column shows iso volumetric contraction (I. C.), 2^(nd) column showsejection, 3^(rd) column shows early filling and 4^(th) column shows latefilling.

FIG. 6 displays flow in a normal LV at early filling peak obtained suingecho-CDV. The streamline color indicates the velocity magnitude whereasthe colored ellipses show the location and size of the intraventricularvortex cores.

FIG. 7 displays an exemplary study design where a factorial 3(positions)×3 (speeds)×3 (degrees of LV dysfunction) experiment isperformed in a porcine model (n=10) of acute heart failure induced bycoronary microsphere embolization. This design allows for creation of alarge matrix of the studied parameters (LV function, position and speedcombinations) and the measured flow and hemolysis metrics.

FIG. 8 displays different LVAD positions. 1st row shows TEEmid-esophageal 135 degrees view sketch and 2^(nd) row shows TTEparasternal long-axis view sketch. 1st column shows Position A, 2^(nd)column shows Position B and 3^(rd) column shows Position C.

FIG. 9 displays the echocardiographic acquisition and post-processingmethodology which include, 2D+t flow reconstruction, intraventricularvortex tracking, blood residence time, transport barriers and E/A wavetracking.

FIG. 10 displays phase contrast MRI blood flow maps in a human leftventricle during early filling (left) and at aortic valve opening(right). Clockwise and counter-clockwise vortices are represented bygreen and magenta ellipses, respectively.

FIG. 11 displays velocity maps and vortex properties. Panel A showsvelocity maps with vortices highlighted for a LVAD case (1st column), adilated cardiomyopathy case (2nd column) and a healthy control case (3rdcolumn) at different time instants within the cardiac cycle (rows as %of RR interval). The blue-green colors and black arrows indicate theinstantaneous velocity magnitude and direction. The red (and white)ellipses represent the main clockwise (and secondary counter-clockwise)vortices. Panel B shows boxplots and scatter plots of vortex properties(circulation Γ_(CW), radius R_(CW) and longitudinal position X_(CW) ofthe clockwise main vortex) for patients with LVAD support (blue),dilated cardiomyopathy patients (orange) and healthy controls (green).Panel C shows velocity pulsatility (VP) maps for the same cases of PanelA; white arrows represent the time-averaged velocity field. Panels Dshows boxplots and scatter plots of velocity pulsatility index (VPI) forthe same groups of Panel B.

FIG. 12 displays residence time. Panel A shows residence time maps atpeak R-wave after 5 seconds of integration for the same cases of FIG.11A; black arrows indicate the velocity instantaneous magnitude anddirection. Panel B shows boxplots and scatter plot of the instantaneousspace-averaged residence time at peak R-wave after 5 seconds ofintegration for the same groups of FIG. 11B.

FIG. 13 displays cumulative shear. Panel A shows cumulative shear index(CSI) maps at peak R-wave after 5 seconds of integration for the samecases of FIG. 11A. Panel B shows boxplots and scatter plot of theinstantaneous maximum CSI at peak R-wave after 5 seconds of integrationfor the same groups of FIG. 11B.

FIG. 14 displays T_(R) and CSI in LVAD-support with aorticinsufficiency. Panel A-B shows residence time maps (A) and cumulativeshear index maps (B) for a representative LVAD-implanted patient withsevere aortic insufficiency at different time instants within thecardiac cycle (as % of RR interval). The checkered region highlightsregurgitant blood entering the LV though the aortic valve. Panel C-Dshows boxplots and scatter plots of the space-averaged residence time(C) and size of the high-shear region (CSI>200/s) (D) at peak R-waveafter 5 seconds of integration grouped according to the degree of aorticinsufficiency.

FIG. 15 displays ramp study where velocity (A), residence time (B),cumulative shear index (C) and velocity pulsatility (D) maps for asample LVAD-implanted patient at different pump speeds (columns) at peakR-wave after 5 seconds of integration.

DETAILED DESCRIPTION

A left ventricular assist device (LVAD) is a type of heart pump ormechanical circulatory support device implanted in selected patients.LVADs have been demonstrated to provide a safe and effective mechanicalsupport in patients undergoing high-risk revascularization proceduresand in patients with cardiogenic shock related to myocardial infarction.LVADs have also been demonstrated to be effective as bridge totransplantation or destination therapy in patients with end stage heartfailure. Nonlimiting examples of left ventricular assist devices includeHeartmate, Jarvik, Thoratec VAD, CentriMag, HeartWare, CorWave andImpella. Heartmate is an intermediate-to-chronic LVAD developed with thegoal of providing up to 10 years of circulatory support for a broadrange of advanced heart failure patients. Jarkvik augments the weakenedheart's blood output to help restore a normal blood flow throughout thebody and Thoratec is a device ideal for patients requiring extendedleft, right, or biventricular support. CentriMag, also known asLevitronix, is a temporary external VAD designed to be used as ashort-term solution for acute heart failure while longer-term optionsare considered. HeartWare is a miniaturized pump capable of deliveringup to 10 liters/minute of blood flow from the heart to the rest of thebody and is being used in clinical trials for both bridge totransplantation and destination therapy. Impella is a minimally invasivecardiac assist device designed to partially unload the left ventriclethus reducing the heart's workload and oxygen consumption. CorWave is anLVAD that uses a pulsating membrane instead of a conventional pump.

In the LV of a diseased heart, progressive adverse remodeling leads toabnormal flow patterns that may impair pumping efficiency, and thereforeaffect the blood transit within the ventricle. Without wishing to bebound by theory, it is believed these abnormal intraventricular flowdynamics may contribute to the progression of certain diseases, leadingto a final stage of heart failure (HF) (26, 27). Thus, it has beenrecognized that a deeper understanding of LV blood flow dynamics innormal and diseased LVs may enhance the current characterization ofcardiac physiology and lead to a better knowledge of the pathophysiologyof heart failure, facilitate subclinical diagnosis of cardiac diseases,improve tools used for characterizing, predict risk of thrombusformation and guide treatment strategies.

The present disclosure is based, in part, on the discovery of novel flowimage-based method to identify advantageous or beneficial positioningand/or settings of LVADs that maximizes device stability, performance,and intraventricular blood transport, while minimizing hemolysis andintraventricular stasis risk. In some embodiments, provided herein aremethods to assess the location and extent of intraventricular stasisregions inside a cardiac chamber or blood vessel (e.g., intraventricularstasis regions in a subject having a LVAD) by digital processingflow-velocity images obtained either by phase-contrast magneticresonance (PCMR), 2D color-Doppler velocimetry (echo-CDV),echo-particle-image-velocimetry (echo-PIV), synthetic apertureultrasound imaging, ultrasound vector velocimetry by transverseoscillation, direct PIV obtained by optical scanning of natural orartificial blood flow tracers. In general, any method suitable forproviding a spatio-temporal distribution of flow velocity inside thecardiovascular system can be used. Approaches provided herein are based,at least in part, on quantifying the distribution of the blood ResidenceTime (TR) from time-resolved blood velocity fields in the cardiacchamber or blood vessel. In some aspects, methods provided herein enablein-vivo assessment of the location and extent of the stasis regions inthe LV cardiac chamber or blood vessel (e.g., in a subject having aLVAD). Original metrics developed to integrate flow properties intosimple scalars suitable for a robust and personalized assessment of therisk of thrombosis are provided herein. The early prediction of bloodstasis in a cardiac chamber or blood vessel (e.g., in a subject having aLVAD) allows for directed use of anticoagulant or other (e.g.,mechanical, surgical, or electrophysiological) therapy for the purposeof primary and secondary prevention, which, ultimately, result in adecreased occurrence of strokes.

The early prediction of blood stasis in a cardiac chamber or bloodvessel (e.g., in a subject having a LVAD) may result in a decrease instrokes by appropriate use of anticoagulant therapy, appropriate use ofmechanical surgical or procedural treatments to remove or alter cardiacstructures or exclude blood flow from structures via intracardiac orextracardiac devices, or appropriate use of electrophysiologic surgicalor procedural therapies to alter and/or ablate electrical heart rhythmsand/or conduction patterns in the heart (including atrial fibrillationablation) for the purpose of primary and secondary prevention. It mayalso have a significant impact on left ventricular assist device (LVAD)device design and operation set-up. For example, LVAD positioning,speed, and/or other operating variable may be adjusted based on theresults obtained by using methods described herein, and the risk forhemolysis and/or thrombosis in subjects having a LVAD can be minimized.

In certain embodiments, methods disclosed herein include directmeasurement of blood flow inside the cardiac chambers (e.g., in subjecthaving a LVAD), instead of on numerical simulations of said flow, whichare computationally expensive, and usually rely on geometricaloversimplifications about the heart's anatomy (e.g. valves, papillarymuscles, trabeculae carnae, etc.), as well as oversimplified models ofblood rheology. In some aspects, methods provided herein are based onthe solution of a transport equation to obtain the spatiotemporaldistribution of residence time inside the cardiac chambers, which ismuch more efficient than releasing virtual particles and tracking theirtrajectories. The approach can be used to analyze cardiac imaging dataobtained using standard modalities. These innovations make the disclosedmethod more reliable and better suited for 1) high-throughput clinicaluse and seamless integration within existing medical imaging devices andsoftware tools, 2) evaluation of blood stasis and hemolysis in the fourcardiac chambers rather than just in the left ventricle.

In some aspects, methods disclosed herein (e.g., methods for identifyingregions of blood flow stasis inside a cardiac chamber or blood vessel ofa subject with a LVAD, methods for evaluating intraventricular flowshear stresses and their dependence on LVAD pump speed and cannulaplacement, or methods for calculating blood transport inside any cardiacchamber or blood vessel of a subject having a LVAD) include identifyingregions of blood flow stasis inside a cardiac chamber or blood vessel ofa subject having an implanted LVAD by obtaining flow-velocity images ofblood inside a cardiac chamber or blood vessel of the subject, andcalculating the residence time (TR), the standard deviation of theresidence time (σR), kinetic energy, and/or rate of distortion of bloodparticles. As used herein, a “blood particle” is defined as a fluidparcel of blood containing a very small amount of fluid that isidentifiable throughout its dynamic history while moving with the bloodflow.

In some embodiments, generating numerical metrics of blood flowcomprises calculating the blood flow's residence time (TR) inside thecardiac chamber or blood vessel (e.g., in subject having a LVAD). Insome embodiments, generating numerical metrics of blood flow comprisescalculating the standard deviation of the residence time (σR) inside thecardiac chamber or blood vessel. In some embodiments, generatingnumerical metrics of blood flow comprises calculating both the bloodflow's residence time (TR) and the standard deviation of the residencetime (σR) inside the cardiac chamber or blood vessel. In someembodiments, generating numerical metrics of blood flow comprisescomparing the flow's residence time (TR) versus its standard deviation(σR) inside the cardiac chamber or blood vessel. In some embodiments, inregions of a cardiac chamber or blood vessel where TR is high comparedto σR, the identification and/or estimation of blood stasis isstatistically more significant than in regions where TR is low comparedto R. In some embodiments, regions of a cardiac chamber or blood vesselwhere TR−σR, or TR−

2σ

R and/or TR−

3σ

R, etc. are higher than a reference value (e.g., the value of TRobserved in a cohort of patients that developed a thrombus in a clinicalstudy) are identified as regions of blood flow stasis. In someembodiments, regions of blood flow stasis are identified with astatistical significance of about 70%, 71%, 72%, 73%, 74%, 75%, 76%,77%, 78%, 79%, 80%, 81%, 82%, 83%, 84%, 85%, 86%, 87%, 88%, 89%, 90%,91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, 99.1%, 99.2%, 99.3%, 99.4%,99.5%, 99.6%, 99.7%, 99.8%, 99.9% or greater. In some embodiments,regions of blood flow stasis that are identified with statisticalsignificance are predictive of risk of intracardiac or intravascularthrombus or of embolism (e.g., in a subject having a LVAD). In someembodiments, in regions of a cardiac chamber or blood vessel where theratio of TR to σR is higher than a reference ratio of TR to σR (e.g.,the ratio of TR to σR observed in a cardiac chamber or blood vessel of ahealthy subject), the identification and/or estimation of blood stasisis statistically more certain than where the ratio of TR to σ(R) isabout the same or lower than the reference ratio of TR to σR. In someembodiments, regions of a cardiac chamber or blood vessel where theratio of TR to σR is high compared to a reference ratio (e.g., the ratioof TR to σR observed in a cardiac chamber or blood vessel of a healthysubject) are identified as regions of blood flow stasis, and arepredictive of risk of intracardiac or intravascular thrombus or ofembolism (e.g., in subject having a LVAD). In some embodiments, theobserved ratio of TR to σR measured by using methods described herein isused (e.g., as a sole parameter or as one of several parameters) toguide LVAD positioning, speed, and/or other operating variable to reducethe risk for hemolysis and/or thrombosis in subjects having a LVAD.

In some embodiments, generating numerical metrics of blood flow (e.g.,in subject having a LVAD) comprises calculating additional descriptorsof the probability distribution of the values of the residence time(e.g., skewness, kurtosis, median, inter-quartile range and/or otherinter-percentile ranges) at each point in space and instant in time, inorder to estimate the statistical significance of the calculated valuesof TR.

In some embodiments, generating numerical metrics of blood flowcomprises calculating the blood flow's kinetic energy inside the cardiacchamber or blood vessel (e.g., in subject having a LVAD). Kinetic energymeasures the overall rate of motion of the blood particles inside ablood region. In some embodiments, low values of kinetic energy in aresidual blood region (e.g., a blood region with high residence time)indicate that such region is stagnant and, therefore, prone tothrombosis. In some embodiments, generating numerical metrics of bloodflow comprises calculating the standard deviation of the blood flow'skinetic energy inside the cardiac chamber or blood vessel. In someembodiments, generating numerical metrics of blood flow comprisescalculating both the blood flow's kinetic energy and the standarddeviation of the blood flow's kinetic energy inside the cardiac chamberor blood vessel. In some embodiments, a kinetic energy that is lowcompared to the standard of deviation of kinetic energy is indicative ofblood flow stasis, and is predictive of risk of intracardiac orintravascular thrombus or of embolism (e.g., in subject having a LVAD).In some embodiments, observed kinetic energy measured by using methodsdescribed herein is used (e.g., as a sole parameter or as one of severalparameters) to guide LVAD positioning, speed, and/or other operatingvariable to reduce the risk for hemolysis and/or thrombosis in subjectshaving a LVAD.

In some embodiments, generating numerical metrics of blood flowcomprises calculating the blood flow's rate of distortion inside thecardiac chamber or blood vessel (e.g., in subject having a LVAD). Therate of distortion measures the rate at which the distances of adjacentblood particles change with time in the neighborhood of a given bloodparticle. In some embodiments, low values of rate of distortion in aresidual blood region (e.g., a blood region with high residence time)indicate that such region is stagnant and, therefore, prone tothrombosis. In some embodiments, generating numerical metrics of bloodflow comprises calculating the standard deviation of the blood flow'srate of distortion inside the cardiac chamber or blood vessel. In someembodiments, generating numerical metrics of blood flow comprisescalculating both the blood flow's rate of distortion and the standarddeviation of the blood flow's rate of distortion inside the cardiacchamber or blood vessel. In some embodiments, a rate of distortion thatis low compared to the standard of deviation of the rate of distortionis indicative of blood flow stasis, and is predictive of risk ofintracardiac or intravascular thrombus or of embolism (e.g., in subjecthaving a LVAD). In some embodiments, an observed rate of distortionmeasured by using methods described herein is used (e.g., as a soleparameter or as one of several parameters) to guide LVAD positioning,speed, and/or other operating variable to reduce the risk for hemolysisand/or thrombosis in subjects having a LVAD.

In some embodiments, generating numerical metrics of blood flowcomprises calculating a blood stasis timescale index (e.g., in subjecthaving a LVAD). As used herein, a “blood stasis timescale index” is anindex that is inversely related to the rate of distortion, and thatmeasures the amount of it that takes the flow to deform a given bloodparticle by an amount comparable to the size of the blood particle. Insome embodiments, high values of a blood stasis timescale index in aresidual blood region (e.g., a blood region with high residence time)indicate that such region is stagnant and, therefore, prone tothrombosis.

In some aspects, methods disclosed herein utilize a spatiotemporalvelocity map of blood flow in the heart as the input, together withanatomical images that are used to segment the walls of the cardiacchambers (e.g., in subject having a LVAD). This data may be obtainedusing color Doppler echocardiographic imaging, MRI with 4D flow, orother medical imaging techniques that provide velocity maps. The inputdata can consist of 2D or 3D time-resolved image data. The velocity datacan be used to solve a transport equation with unit forcing using thesegmented wall positions to impose no penetration boundary conditions.This solver provides the spatiotemporal distribution of the bloodresidence time inside the cardiac chambers (TR). The residence timedistribution can be analyzed using spatiotemporal clustering algorithmsto identify residual regions with relative decreased mixing fromincoming flow.

In some aspects, methods disclosed herein (e.g., methods for identifyingregions of blood flow stasis inside a cardiac chamber or blood vessel ofa subject, methods for estimating risk of intracardiac or intravascularthrombus or of embolism originating in a cardiac chamber or blood vesselin a subject, or methods for calculating blood transport inside anycardiac chamber or blood vessel of a subject having a LVAD) includegenerating a residence time (TR) map, a kinetic energy map, and/or arate of distortion map. In some embodiments, such maps are generatedusing numerical metrics of blood flow (e.g., numerical metrics ofresidence time (TR), kinetic energy, and/or rate of distortion of bloodparticles obtained from one or more flow-velocity images) to identifyand characterize regions of blood flow stasis. In some embodiments, suchmaps are used to guide LVAD positioning, speed, and/or other operatingvariable to reduce the risk for hemolysis and/or thrombosis in subjectshaving a LVAD.

In some embodiments, methods disclosed herein include generating a mapof the standard deviation of the residence time (σR), a map of thestandard deviation of kinetic energy, and/or a map of the standarddeviation of the rate of distortion (e.g., in subject having a LVAD). Insome embodiments, such maps are generated using numerical metrics ofblood flow (e.g., numerical metrics of the standard deviation of theresidence time (σR), the standard deviation of kinetic energy, and/orthe standard deviation of the rate of distortion of blood particlesobtained from one or more flow-velocity images) to identify andcharacterize regions of blood flow stasis, particularly theirstatistical significance. In some embodiments, such maps are used toguide LVAD positioning, speed, and/or other operating variable to reducethe risk for hemolysis and/or thrombosis in subjects having a LVAD.

In some embodiments, a medical image-based apparatus is operated toobtain multiple flow-velocity images performed with different velocityscales (e.g., the encoding velocity in phase contrast MRI or the colorscale in Doppler echocardiography). In some embodiments, one or moreflow-velocity images are performed with velocity scales that aresignificantly lower than the scales that are typically used (e.g., about20 percent, about 25 percent, about 30 percent, about 35 percent, about40 percent, about 45 percent, about 50 percent, about 55 percent, about60 percent, about 65 percent, about 70 percent, about 75 percent, about80 percent, or more lower than the scales that are typically used), inaddition to one or more flow-velocity images that are performed with thetypically-used velocity scales. In some embodiments, the data from theobtained multiple flow-velocity images are retrospectively merged inorder to expand the dynamical range of the velocity measurements. Insome embodiments, data from the obtained flow-velocity images areretrospectively merged to generate residence time (TR), kinetic energy,and/or rate of distortion maps. In some embodiments, data from theobtained flow-velocity images are retrospectively merged to generatemaps of standard deviation of residence time (σR), standard deviation ofkinetic energy, and/or standard deviation of rate of distortion.Obtaining multiple flow-velocity images as described herein is useful inpreventing overestimation of the residence time when there are regionswhere the blood velocity falls below the minimum measurable velocity ofa single velocity scale acquisition (e.g., a velocity scale acquisitionthat is typically used). In some embodiments, the medical image-basedapparatus is operated to obtain 2, 3, 4, 5, 6, 7, 8, 9, 10 or moreflow-velocity images (e.g., one, two, or three-dimensional flow-velocityimages resolved in time) performed with different velocity scales. Insome embodiments, these residence time and flow velocity maps are thenfurther processed to provide numerical metrics of blood stasis and thelocations of regions with increased stasis. For example, the bloodflow's kinetic energy, defined as K=½(u2+v2+w2), where u, v and w arethe three components of the flow velocity in an orthogonal coordinatesystem, can be determined. However, kinetic energy is not a Galileaninvariant and it could be possible for a fluid parcel to have highvalues of K while moving with little distortion, similar to a rigidsolid. Thus, the distortion of fluid particles, which is quantified bythe second invariant of the symmetric strain tensor,Q_(ij)=(du_(i)/dx_(j)+du_(j)/dx_(i))/2, can also be computed. For anincompressible flow, the first invariant of S_(ij) is zero and thesecond invariant is defined as Q_(S)=trace (S_(ij)2)/2. Note that Q_(S)has dimensions of squared inverse of time, so it can be used to define asecond stasis timescale T_(S)=Q_(S) ^(−1/2) in addition to TR.

In some embodiments, the size, position, shape, mobility, distance tocardiac wall, average kinetic energy and average distortion time of eachspatio-temporally clustered residual volume are measured as a functionof time (e.g., in subject having a LVAD). In some embodiments,colocalization and relative values of different metrics are alsoanalyzed. Together with the number of residual volumes, this analysisprovides a set of parameters that can be used to build apatient-specific risk index of blood stasis and risk of thrombusformation in the cardiac chambers (e.g., in subject having a LVAD) basedon non-invasive clinical images. In some embodiments, this analysisprovides a set of parameters that can be used to guide LVAD positioning,speed, and/or other operating variable to reduce the risk for hemolysisand/or thrombosis in subjects having a LVAD.

In some embodiments, provided herein are methods useful for thecharacterization (e.g., clinical evaluation, diagnosis, classification,prediction, profiling) of a subject's risk of intracardiac thrombusformation and for predicting whether and to what extent the subject maybenefit from treatment. In some embodiments, provided herein are methodsuseful for the characterization (e.g., clinical evaluation, diagnosis,classification, prediction, profiling) of a subject's risk ofintracardiac thrombus formation after having been implanted with a LVAD.As used herein, diagnosing includes both diagnosing and aiding indiagnosing. Other diagnostic criteria may be evaluated in conjunctionwith the results of methods provided herein in order to make adiagnosis. In some embodiments, a diagnosis can be used to guide LVADpositioning, speed, and/or other operating variable to reduce the riskfor hemolysis and/or thrombosis in subjects having a LVAD.

The term “subject” refers to an animal or human. Preferably, the subjectis a human. Subjects can also include non-human mammals. A human subjectcan be known as a patient. In some embodiments, the patient isexperiencing or known to have experienced in sinus rhythm with LVsystolic dysfunction. Such patients are known to be at increased risk ofthrombus formation and subsequent embolic events (e.g. stroke) butcurrently the vast majority of them are not being identified and treatedwith any anticoagulation therapy, resulting in a high degree ofmorbidity and mortality. In some embodiments, the patient has beenimplanted with a LVAD.

In some embodiments, the patient is experiencing or known to haveexperienced atrial fibrillation. Currently, such patients arerisk-stratified based only on the basis of demographic and comorbiditydata based on previous cohorts, but no patient-specific tools exist tooptimally determine for which patients the risk/benefit ofanticoagulation is favorable.

In some embodiments, the patient has an implanted left ventricularassist device (LVAD) and is at increased risk of thrombus formation.Thrombi in these patients can cause systemic emboli as well as LVADdysfunction. In some embodiments, methods provided herein are used todetermine: 1) pre-surgical optimization of device selection, 2)optimization of device implantation, 3) optimization of LVAD settingsincluding, but not limited to, pump speed alteration, pump speedmodulation, and the use of pump settings to generate intermittentpulsatile flow, and 4) identification of patients for whom therisk/benefit of anticoagulation therapy is favorable.

In some embodiments, provided herein are methods for the communicationof results or diagnoses or both to technicians, physicians or patients.In certain embodiments, computers are used to communicate assay resultsor diagnoses or both to interested parties, e.g., physicians and theirpatients. In some embodiments, a diagnosis or result (e.g., resultindicating the effectiveness or risk of LVAD positioning or settings) iscommunicated to the subject as soon as possible after the diagnosis isobtained. The diagnosis or result may be communicated to the subject bythe subject's treating physician. Additionally or alternatively, thediagnosis or result may be sent to a test subject by email orcommunicated to the subject by phone. The diagnosis may be sent to atest subject by in the form of a report. A computer may be used tocommunicate the diagnosis or result by email or phone. In certainembodiments, the message containing diagnosis or result may be generatedand delivered automatically to the subject using a combination ofcomputer hardware and software which will be familiar to artisansskilled in telecommunications.

The terms “decrease”, “decreased”, “reduced”, “reduction” or‘down-regulated” are all used herein generally to mean a decrease by astatistically significant amount. However, for avoidance of doubt,“reduced”, “reduction”, “decreased” or “decrease” means a decrease by atleast 10% as compared to a reference level, for example a decrease by atleast about 20%, or at least about 30%, or at least about 40%, or atleast about 50%, or at least about 60%, or at least about 70%, or atleast about 80%, or at least about 90% or up to and including a 100%decrease (i.e. absent level as compared to a reference sample), or anydecrease between 10-100% as compared to a reference level, or at leastabout a 0.5-fold, or at least about a 1.0-fold, or at least about a1.2-fold, or at least about a 1.5-fold, or at least about a 2-fold, orat least about a 3-fold, or at least about a 4-fold, or at least about a5-fold or at least about a 10-fold decrease, or any decrease between1.0-fold and 10-fold or greater as compared to a reference level.

The terms “increased”, “increase” or “up-regulated” are all used hereinto generally mean an increase by a statistically significant amount; forthe avoidance of any doubt, the terms “increased” or “increase” means anincrease of at least 10% as compared to a reference level, for examplean increase of at least about 20%, or at least about 30%, or at leastabout 40%, or at least about 50%, or at least about 60%, or at leastabout 70%, or at least about 80%, or at least about 90% or up to andincluding a 100% increase or any increase between 10-100% as compared toa reference level, or at least about a 0.5-fold, or at least about a1.0-fold, or at least about a 1.2-fold, or at least about a 1.5-fold, orat least about a 2-fold, or at least about a 3-fold, or at least about a4-fold, or at least about a 5-fold or at least about a 10-fold increase,or any increase between 1.0-fold and 10-fold or greater as compared to areference level.

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EXAMPLES

The invention is further described in the following examples, which donot limit the scope of the invention described in the claims.

Example 1

The present study is designed to implement a novel method for evaluatingintraventricular flow shear stress and for measuring and mapping bloodstasis in the heart. The purpose is to obtain individual quantitativemetrics of global and regional stasis from flow-velocity measurements inthe LV. The feasibility of the method is first tested by comparinghigh-resolution datasets of LV flow velocity by both 2D echo-CDV andphase-contrast magnetic resonance (PCMRI). To generalize theapplicability of the tool, the method is also adapted to work withultrasound data. Data from LVs before and after LVAD implantation isanalyzed. The unique ability of the tool to identify and quantifycumulative blood shear stress, assess the risk of hemolysis, trackregions at risk of blood stagnation, and provide qualitative andtopological assessments of blood stasis in the LV is demonstrated.

Methods

Study Population

100 patients implanted with HeartWare HVAD devices prospectivelyparticipate in this study and provide echocardiography studies for 2Dcolor Doppler velocimetry (echo-CDV) evaluation. For each patient,studies collected at the following timepoints are analyzed:

-   -   Baseline (prior to implant)    -   Implant—while in operating room.

Two abbreviated transesophageal echos:

-   -   1) after implantation/once patient is off cardio-pulmonary        bypass while chest is still open,    -   2) after chest closure.    -   Discharge (with Lavare on and off).    -   3 months post-implant.    -   6 months post-implant, including a ramp study with abbreviated        echos for flow velocimetry acquired every 200 rpms.    -   12 months post-implant.

All the echocardiographic studies from each patient is analyzed todetermine 2D velocity maps and derive a comprehensive database of flowparameters (vortex position, size and strength, blood shear mapping,residence time, pressure gradients, etc).

In order to evaluate the dependence on cannula positioning of hemolysis,blood stasis and other flow parameters that may correlate with outcomes,cannula positioning is imaged and parameterized with respect to LVanatomical features and also with respect to intraventricular flowfeatures (e.g. the inflow jet).

Data from clinically indicated blood tests are collected from electronicmedical records, including (if/when available) measures of hemolysis(Hb, LDH, plasma free-Hb), and basic lab samples including Hb,whitecount, platelets, Na, K, creatinine, BUN, liver function tests(LFTs). Data on complications (bleeding, thrombotic complications,worsening heart failure) are collected from the electronic medicalrecords. Also, information regarding clinical outcomes (survival, needfor additional mechanical support, need for heart transplantation,duration of hospital stays) is collected.

These data are analyzed to glean multivariate correlation and causalityrelationships between themselves and with cannula positioning, LVADspeed and flow parameters.

2D Echo Color Doppler Velocimetry.

The 2D echo-CDV algorithm analyzes standard color-Doppler sequences andprovides time-resolved vector flow maps in the apical long axis view ofthe LV (defined by the apex and the center of the mitral and of theaortic valves)(7, 21). Patients routinely undergo echocardiograms aspart of their standard care.

Echo-CDV only requires a few additional images, extending the durationof the study by˜5 minutes (21). Echo-CDV with phase-contrast wasrecently validated MRI in patients, obtaining good agreement between thetwo modalities (12) (FIG. 1).

Characterization of LV Vortex Patterns.

The flow vorticity, ω, is used to characterize the flow structures andis computed as the curl of the velocity, ω=∇×v. LV vortices areidentified in each instantaneous flow field using the second invariantof the velocity gradient tensor (22, 23). These flow patterns aretracked in time using a clustering algorithm for the analysis ofvortices in turbulent flows (12, 24). They can be characterized by theircirculation, kinetic energy, radius, aspect ratio, and the trajectory oftheir center. Circulation is defined as Γ=

_(Ω)ω(x, y)dΩ, where the 2D domain of integration, Ω is the inner coreof the vortex. The position of the vortex center is {x_(v), y_(v)}=

_(Ω){s, y}ω(x, y)dΩ. The radius of the vortex is defined by

$R = \sqrt{\frac{1}{\Gamma}{\oint_{\Omega}{\left\lbrack {\left( {x - x_{v}} \right)^{2} + \left( {y - y_{v}} \right)^{2}} \right\rbrack{\omega\left( {x,y} \right)}d\;\Omega}}}$Cumulative Blood Shear Stress and Hemolysis

Hemolysis risk is assessed by a power-law model that predicts normalizedhemolysis as

${\frac{\Delta\;{PfHb}}{Hb} = {C{\sum^{a}T_{R}^{b - 1}}}},$where PfHb is the plasma free hemoglobin, Hb is the total hemoglobin inthe blood (intracellular and extracellular), Σ is the cumulative fluidshear stress experienced by blood particles in seconds⁻¹, T_(R) is theirresidence time in seconds (a.k.a. exposure time), and a=2.4, b=0.8 andC=3.6×10AK are empirical constants. In this project, Σ is determinedusing a forced transport equation,

$\begin{matrix}{{\frac{D\sum}{Dt} = {{\partial_{t}{\sum{{+ \nabla} \cdot \left( {v\sum} \right)}}} = S}},} & (1) \\{{{\sum\left( {x,{t = 0}} \right)} = 0},} & \; \\{{{\sum\left( {x_{inlet},t} \right)} = 0},} & \;\end{matrix}$where S is the Von-Mises stress at each point of space and time insidethe left ventricle, determined from the velocity field obtained byecho-CDV in each patient. FIG. 2 shows an example map of Σ obtained froma patient with LV dysfunction. The region of highest cumulative shearcorresponds with the boundary of the LV vortex. Residence time iscomputed in a similar manner as described below.Analysis of Blood Transport Efficiency

Using the time-dependent 2D echo-CDV velocity field v(x, t) and the LVwall tracking data as input, an advection equation is solved for apassive scalar field ψ with uniform initial conditions and step-wiseDirichlet inflow boundary conditions,

$\begin{matrix}{{\frac{D\;\psi}{Dt} = {{{\partial_{t}\psi} + {\nabla{\cdot \left( {v\;\psi} \right)}}} = 0}},} & (2) \\{{{\psi\left( {x,{t = 0}} \right)} = {\psi_{0} = {const}}},} & \; \\{{{\psi\left( {x_{inlet},{0 < t < t_{1}}} \right)} = {\psi_{1} = {const}}},} & \; \\{{{\psi\left( {x_{inlet},{t_{1} \leq t < t_{2}}} \right)} = {\psi_{2} = {const}}},} & \; \\{{etc}.} & \;\end{matrix}$

This approach tags different volumes of blood with different numericalvalues that are transported by the flow, thereby simulating thevisualization of distinct virtual contrast media inside the LV. Forinstance, one can implement a two-step inlet boundary condition to trackthe evolution of the two fluid volumes that enter the ventricle duringthe E wave and the A wave, and to determine the size of these structuresand their frontal position (FIG. 3A).

In addition to tracking the filling transport patterns thespatiotemporal evolution of the blood that is ejected each cardiac cycleis analyzed by integrating equation (2) backwards in time. Combining theresults from the backward and forward integrations allows one toautomatically identify the following transport structures: direct flow(DF, blood that enters and exits the LV in the same cardiac cycle),retained inflow (RI, incoming blood that is not ejected during the samecycle), delayed ejection (DE, ejected blood that entered the LV in aprevious cardiac cycle) and residual flow (RF, blood that entered the LVin a previous cycle and is not ejected in the current cycle, thereforeresiding in the LV for at least two cardiac cycles) (11) (FIG. 3B).

To systematically analyze the effect of LVAD support on LV fillingtransport, the fraction of LV size occupied by the E and A waves as wellas the normalized apical position of each wave's front is determined. Itis possible to combine this approach with our cumulative shearcalculation method to assess the hemolysis risk of the blood pool thatenters the LVAD device each cardiac cycle.

To assess the kinematic efficiency of flow redirection inside the LVunder LVAD support, the size, kinetic energy density and acceleration ofeach transport region at the onset of systole is determined. Kineticenergy density is calculated from 2D echo-CDV data as K(x, t)=|v|²/2.This variable is spatially integrated over the surface occupied by eachtransport region to obtain its overall value inside the region (e.g.K_(DF)=∫_(S) _(DF) K(x)dx). The ratio η_(K)=K_(DF)/K_(LV) at aorticvalve opening in all the patients is calculated to determine if LVADsupport contributes to efficiently focusing the inflow kinetic energyinto the volume of fluid that is ejected during systole. The ratio ofdirect flow area to total LV area in the imaging plane,η_(DF)=S_(DF)/S_(LV), is also computed to quantify the efficiency ofvolumetric blood transport within one cardiac cycle. In addition, theefficiency of flow redirection is assessed by calculating the netacceleration transferred to the direct flow region in the direction ofthe LV outflow tract, normalized with the total magnitude of thisacceleration,

${\eta_{M} = \frac{M_{DF}e_{LVOT}}{M_{DF}}},$where e_(LVOT) is the unitary vector parallel to the direction of the LVoutflow tract, pointing outwards the LV. Fluid acceleration will becalculated as

${M\left( {x,t_{0}} \right)} = {\left( {\frac{\partial v}{\partial t} + {v \cdot {\nabla v}}} \right).}$The orientation of the whole ventricle's M with respect to the LV longaxis indicates the degree of alignment between the hemodynamic pressureforces and the inflow/outflow tract.Blood Residence Time and Stasis.

The time spent by blood particles inside the LV (TR, residence time) iscalculated using a forced transport equation,

$\begin{matrix}{{\frac{{DT}_{R}}{Dt} = {{{\partial_{t}T_{R}} + {\nabla{\cdot \left( {vT}_{R} \right)}}} = 1}},} & (3) \\{{{T_{R}\left( {x,{t = 0}} \right)} = 0},} & \; \\{{{T_{R}\left( {x_{inlet},t} \right)} = 0},} & \;\end{matrix}$as explained previously (18).

The TR distributions of each patient is analyzed for each value of theLVAD speed setting. Residual blood volumes that do not mix with thefresh blood entering the LV each cardiac cycle are automaticallysegmented, which are potentially stagnant.

Spatio-temporally connected pixels with high residence time (higher thana given threshold T₀, e.g. TR>2 sec) are clustered using algorithms (12,24), and stored for further analysis. For each segmented residualvolume, the spatiotemporally averaged stasis indices such as kineticenergy are calculated. For each segmented residual volume, stasisindices such as the kinetic energy (K) or the distortion timescaleT_(S)=√{square root over (1/Q_(S))}¹³ is calculated, where Q_(S) is the2nd invariant of the fluid's symmetric strain tensor S (25). Low Kor/and high T_(S) are indicators of blood stasis.

This methodology is illustrated for the diseased LV shown in FIG. 4,where two residual blood volumes with TR>2 sec were identified. Thesedata and recent work (18) suggest that the proposed analysis is able toidentify blood volumes that are at high risk of stasis.

Mapping Hemodynamic Pressure Gradients.

An algorithm to calculate pressure maps from echo 2D flow velocity datahas been calculated. The algorithm is based on enforcing massconservation and leads to the integration of a Poisson equation for thepressure p, with boundary conditions on the moving walls of the LV.

$\begin{matrix}{{{\nabla^{2}p} = {{- \nabla} \cdot \left( {v \cdot {\nabla v}} \right)}},{{inside}\mspace{14mu}{the}\mspace{14mu}{LV}}} & (4) \\{{{{{\nabla p} \cdot n} = {{- \left\lbrack {\frac{\partial v}{\partial t} + {v \cdot {\nabla v}}} \right\rbrack} \cdot n}},{{at}\mspace{14mu}{the}\mspace{14mu}{LV}\mspace{14mu}{walls}},}\;} & \;\end{matrix}$where n is the vector perpendicular to the LV walls at each position ofthe wall. This equation is integrated using a numerically efficientmultigrid method and the boundary conditions are imposed using a sharpinterface immersed boundary method. FIG. 5 shows an example of thepressure maps obtained by our algorithm from echocardiographic imaging.Cannula Positioning.

Cannula positioning is imaged by echocardiography in the parasternal (ormid-esophageal for intraoperative imaging) long axis view. Its positionis parameterized by the distance between the aortic valve and the tip ofthe cannula is measured and normalized with the long axis length of theventricle. The normalized distance of the cannula to the inferolateraland anteroseptal walls of the LV is measured and used to parameterizecannula positioning. In addition to the orientation of the cannula withrespect to anatomical structures, it is postulated that its orientationwith respect to flow structures may be a relevant parameter thatdictates shear stresses, residence time, etc. Thus, the distance andrelative orientation between the cannula and the axis of the flowfilling jet of the LV is also determined.

Summary

The main objective of this exploratory study is non-invasivequantification of intraventricular flow using echo to better understandhow the speed of the HeartWare HVAD device and its placement affect therisk of thrombus formation, hemolysis, and patient outcomes. A secondaryobjective of this work is to assess whether non-invasive blood flowimaging could be incorporated as a tool to guide device implantation andclinically manage HVAD implanted patients. To achieve this objective,echocardiographic studies on a subgroup of ˜100 patients implanted withthe HVAD enrolled in The HeartWare MCS Destination Therapy Post-ApprovalStudy were analyzed. Novel software to quantify the blood flow velocityfields in the LV of these patients is used. These data are used tocharacterize the dynamics of LV blood flow patterns (e.g. diastolicvortices), the efficiency of blood transport, the LV residence time ofblood and the cumulative shear stress experienced by blood cells. Theseparameters are correlated to clinical data including blood labwork andoutcome data (hemolysis, thrombosis).

Example 2

The present study is designed to determine the effects of position andspeed setting of the Impella system on 1) intraventricular flowpatterns, 2) hemolysis, 3) intraventricular blood stasis, and 4) itsimpact on blood transport and left ventricular filling. To achieve thisobjective, an experimental study is performed in a porcine model (n=10)using a controlled factorial design. Flow and device parameters arecorrelated to the risk of hemolysis by analyzing blood samples in eachof the stages of study. Non-invasive quantification of intraventricularflow using novel imaging techniques such as echo-CDV may be useful toidentify the best settings and locations of the Impella system.

Methods

A total of ten (10) adult minipigs (˜60 kg) undergo instrumentation andflow-imaging experiments. Anesthesia is induced with intravenouspropofol (1.5 mg/kg) and fentanyl (5 μg/kg) and the animals areendotracheally intubated and mechanically ventilated withoutend-expiratory positive pressure. Complete anesthesia is maintained bypropofol (0.2 mg/kg/min) and fentanyl (5-10 mg/kg/h) endovenousinfusion. The abolition of eye reflexes, blood pressure, and heart rateare systematically monitored to ensure deep anesthesia and goodoxygenation and ventilation is ensured by arterial blood gas analysis(28, 29).

Femoral and internal carotid vascular packages are dissected and thecannulation of central arterial and venous access is performed bySeldinger's technique. A right jugular approach is used to place aSwan-Ganz catheter in the pulmonary artery to measure cardiac output.Invasive arterial blood pressure monitoring and arterial blood samplecollection are performed through left carotid artery cannulation. Aftercompleting vascular accesses, anticoagulation is initiated andmaintained with repeated bolus of sodium heparin (100 UI/kg/2 h). Asubxifoid subcutaneous incision is made in order to optimize apicalechocardiographic images (28-31).

Through the right femoral artery an Impella® catheter pump is placed inthe LV and connected to an external console which consists of anintegrated controller for the pump and purge system (Automated Impella®Controler, Abiomed). Impella's placement is guided using transthoracic(TTE) echocardiography in the parasternal long-axis and apical views. Amodified inlet of the Impella® catheter is preferred with a plastic headto avoid undesirable ultrasound reverberations and drop-outs whenacquiring images. Each animal is studied at baseline and after inducingsevere acute left ventricular dysfunction by left main coronarymicrospheres embolization (HF, see FIG. 7) (n=4) as previously reportedin other experiments or our group (28, 32, 33).

A standard 6.5F JL3 coronary artery catheter is advanced via a femoralartery into the left main coronary artery during fluoroscopy.Polystyrene microspheres (45 μm, Polysciences) are diluted with dextranand saline to a solution of 1 mg microspheres per ml. The microspheresolution is injected through the coronary catheter as 5 ml boluses about5 min apart. The embolization is complete when the LV ejection fractionmeasured by 2D echocardiography (Simpson biplane) decrease below 35%.Serial measurements varying the Impella® location and its speed areobtained in baseline, at moderate degrees of LV dysfunction (LV EF 40%)and after 20 min of completing embolization phases (see FIG. 7). Animalsare euthanized at the end of the experiments with intravenoussodium-pentobarbital (100 mg/kg). The local Institute Animal CareCommittee must approve the experimental protocol. All animal proceduresmust be in accordance with guidelines from Directive 2010/63/EU.

Impella® Adjustment of Positioning and Speed

During each of these 3 phases, the location of the catheter is modifiedand placed in the following positions:

1) Position A: The Impella® catheter is set at high thrust condition,lying along the inner curve of the aorta and placing the positioningmarker approximately at the aortic valve. The aim is to settle the pumpinlet approximately 4 cm distal to the aortic valve. The goal is toensure avoiding the subannular position or any position that interfereswith the anterior mitral leaflet or entrain the catheter into thepapillary muscles.

2) Position B: The Impella® catheter is arranged with the pump inlet inthe vicinity of the mitral valve apparatus.

3) Position C: The Impella® catheter is positioned deep inside the LVwith the pump outlet in the vicinity of the aortic valve leaflets. Ineach position, the catheter speed is varied 3 times (according to 50%,75% and 100% of the maximum pump speed). See FIGS. 7-8.

Hemolysis Study

A pair of 2 mL blood samples is collected simultaneously from the distalend of the Swan-Ganz catheter (proximal pulmonary artery) and from theright internal carotid artery sheet after 5 minutes of eachphase/position/velocity combination. Complete blood counts (leukocyte,platelet, and erythrocytes) are determined using a hematology analyzer.Total hemoglobin and hematocrit are measured. The plasma-free hemoglobin(pfHb) is calculated by the Harboe direct spectrophotometric method toquantify hemolysis (34). 1 mL aliquots of blood are centrifuged toprepare platelet-poor plasma (PPP). 100 μL PPP is diluted with 1 mL 0.1%Na2CO3 solution (Sigma-Aldrich, St. Louis, Mo., USA). Eq. 1 details thecalculation of pfHb concentration. Absorbance is measured using aUV/visible spectrophotometer (NanoPhotometer, IMPLEN).

$\begin{matrix}{{{pfHb}\left( \frac{g}{L} \right)} = {\left( {{167.2 \times A_{415}} - {83.6 \times A_{380}} - {83.6 \times A_{450}}} \right) \times \frac{1}{1000} \times {1/\frac{{Vol}_{plasma}}{{Vol}_{{Na}_{2}{CO}_{2}}}}}} & \left( {{Eq}.\mspace{14mu} 1} \right)\end{matrix}$where A₄₁₅ is the sample absorbance at 415 nm, A₃₈₀ is the sampleabsorbance at 380 nm and A₄₅₀ is sample absorbance at 450 nm. The indexof hemolysis (IH) (35) is used to evaluate the experimental data,

$\begin{matrix}{{{IH}\mspace{14mu}(\%)} = {\frac{\left( {1 - \frac{H_{ct}}{100}} \right)\frac{pfHb}{1000}}{H_{b}} \times 100}} & \left( {{Eq}.\mspace{14mu} 2} \right)\end{matrix}$where H_(ct) is the hematocrit value of the blood expressed in %, pfHbis the concentration of plasma-free hemoglobin (unit: mg/dL), and Hb isthe hemoglobin concentration of the whole blood (unit: g/dL). Thedifference of PFH between the outlet blood sample (carotid artery) andinlet blood sample (pulmonary artery) is used to evaluate shear-inducedhemolysis, IH_(flow)=IH_(outlet)−IH_(inlet).Image Acquisition and Processing

All the Image acquisition and post-processing methods are depicted inFIG. 9. TTE echocardiographic examinations are performed using a Vivid 7scanner and phase-array 2-4 MHz transducers (GE Healthcare).Three-dimensional sequences are obtained from apical views to ensurecomplete apical visualization without foreshortening and are used tomeasure LV volumes and ejection fractions. Longitudinal, radial andcircumferential myocardial strain and strain-rate is measured fromapical long-axis and parasternal short axis sequences (EchoPac version110.1.2, GE Healthcare).

2D+t Flow reconstruction: Color-Doppler velocimetry (Echo-CDV) is usedto obtain the unsteady two-dimensional (2D+t) flow field as previouslydescribed and validated ((20, 36-38, 39-41), FIG. 9a ).

For this purpose, consecutively color-Doppler sequences of 8 to 14 beatsare acquired, followed by a 2D cine-loop (4-7 beats) at high frame-ratewithout moving the probe. Echo-CDV provides the crossbeam flow velocityby integrating the continuity equation, under a planar flow assumption,imposing a condition of non-flow penetration at the myocardium-bloodinterface.

Intraventricular Vortex Tracking: In 2-D, the three-dimensional (3-D) LVvortex ring is visualized as two cores corresponding to theintersections between the fluid structure and the imaging plane, withthe clockwise rotating section (main) directed toward the anteroseptalwall and the counterclockwise section (secondary) close to theinferolateral LV wall (36, 40) (FIGS. 6 & 9 b). Vortex core sections aretracked in a threshold-independent manner using the second invariant ofthe velocity gradient tensor of the reconstructed 2-D velocity fields,the Q criterion. Time-evolving in-plane properties of the tracked vortexcores are determined from the flow data obtained on the imaging plane.We measure the in-plane circulation, trajectory, kinetic energy densityand radius of each core ring. These methods have been widely describedby our group (41).

Blood Residence Time: Residence time is defined as the time spent by ablood particle before it leaves the chamber. It has previously beenshown that spatio-temporal maps of residence time can be efficientlyobtained in the LV from 2D+t echo-CDV data by integrating the equationof advection of a passive scalar with unit forcing (20). This equationis solved for 8 consecutive cardiac cycles to ensure temporalconvergence (FIG. 9c ). From the residence time maps, the averageresidence time of the entire blood volume inside the LV is calculated.This is a representative metric of global stasis that accounts for thefull blood pool in the ventricle. However, local stasis metrics may beparticularly meaningful for mural thrombosis. Therefore, blood regionswith a residence time>2 s, hereinafter defined as stagnant regions, arealso identified and tracked. The following features of the stagnantregions are measured: 1) size relative to total LV volume (area in 2D)(dimensionless), 2) mean residence time inside the region (in cycles),and 3) perimeter of contact of the stagnant region with the endocardium(in % of endocardial length). The contact perimeter of stagnant regionswith the endocardium accounts for flow-endocardium interactions thatmost intensively activate the coagulation cascade (42). Stagnant regionsnot spanning a full cardiac cycle or <2% of LV area are dismissed.

Transport Barriers: Blood transport volumes are classified as directflow—blood entering & exiting the LV in the same cardiac cycle—,retained inflow—blood entering in the LV which is not being ejectedduring the same cycle—, delayed ejection—blood ejected in the studiedcycle which entered in the LV during a previous cycle—and residualflow—blood neither entering nor exiting the LV in the studied cycle,therefore spanning in the LV for at least two cardiac cycles—(41,43-47). From the Residence Time maps (FIG. 9c ), we determine thekinetic energy and the size of each transport region in the LV (relativeto ventricular volume, area in 2D) at the onset of ejection (FIG. 9d ).E/A wave tracking: To assess the impact of the Impella device onventricular filling, the residence time maps during diastole areautomatically thresholded to separate and track the blood fractioncarried by the E and A-waves, and determine the size of these structuresand their front location (E/A wave penetration) relative to LV long-axisduring the cardiac cycle ((41), FIG. 9e ).Cumulative Blood Shear Stress and Hemolysis: The risk of plateletactivation inside the LV is calculated using a power-law model where thestress parameter is the cumulative Von-Mises stress Σ experienced byplatelets, is determined H using a forced transport equation,

$\begin{matrix}{{\frac{D\;\Sigma}{Dt} = {{{\partial_{t}\Sigma} + \left( {\nabla{\cdot \Sigma}} \right)} = S}};} & \left( {{Eq}.\mspace{14mu} 3} \right)\end{matrix}$with initial and boundary conditions:H(x,t=0)=0&H(x _(inlet) ,t)=0;  (Eq. 4)where S is the Von-Mises stress at each point of space and time insidethe left ventricle, determined from the velocity field obtained byecho-CDV in each patient.Statistical Analysis

Experimental data is analyzed using linear mixed-effects models, andpaired t-tests where appropriate. The effects of phases, interventionson hemolysis and intraventricular blood transport indices are calculatedas the least-mean square estimates and their standard errors.Differences among the different settings are tested using Dunnett'scontrasts against baseline measurements. This method is particularlywell suited for potentially unbalanced factorial experimental designs asmay be expected in the current proposal in the case all experimentalfactors cannot be replicated in each and every animal.

The association between quantitative variables is assessed by linearmixed-effects models, as well as within-subject correlation coefficientsaccounting for repeated measures (Rrm)(48). The intraclass regressioncoefficient (R_(ic)) and its 95% confidence interval are used to assessagreement. Variables are described as mean±standard deviation.Statistical analysis is performed using R (49). Values of p<0.05 areconsidered significant.

Example 3

The success of left ventricular assist device (LVAD) therapy is hamperedby complications such as thrombosis, bleeding and right heart failure.Understanding blood flow interactions between the heart and the LVADwill help to optimize treatment and decrease complication rates. It ishypothesized that LVADs, by changing flow patterns, modify shearstresses and blood transit in the left ventricular and that thesechanges can be characterized using 2D echo color Doppler velocimetry(echo-CDV).

Echo-CDV and custom post-processing methods were used to map and studyblood flow inside the LV in patients with ongoing LVAD support(Heartmate II, N=7) and compare it to healthy controls and patients withdilated cardiomyopathy (DCM). Intraventricular flow changes were alsoanalyzed during LVAD ramp tests (baseline±400 rpm).

LVAD support reversed the increase in blood stasis associated to DCMwhile it did not reduce intraventricular shear exposure. Within thestudied range, ventricular flow was largely insensitive to moderatechanges in LVAD pump speed. Patients with significant aorticinsufficiency showed abnormalities in blood stasis and shear indices.

This Example shows that echocardiography can be used to obtain detailedinformation about the effect of LVADs on LV flow patterns and bloodtransit. This technique could potentially be used in combination withstandard clinical methods for adjusting LVAD settings in order tooptimize flow transport and minimize stasis on an individual basis.

Left ventricular assist device (LVAD) support is a life-saving therapyfor patients with advanced heart failure (HF) refractory to optimalmedical treatment. The use of LVADs has increased significantly and thetreatment is now widely used both as a bridge to heart transplantationand as destination therapy (1,2). Despite improved survival, majorcomplications such as thrombosis, bleeding and stroke are still common,occurring with an incidence of 8-29% (3-5). The causes of the increasedrisk of thrombosis in LVAD-implanted patients are multifactorial and notfully understood. Nonetheless, intraventricular flow disturbancesleading to abnormal shear stress and blood stasis are recognized asmajor risk factors (6,7), and have been associated with thromboembolicstrokes (8). Of note, recent studies of patients implanted with newgeneration LVADs has shown stroke rates comparable to the oldergeneration of devices despite absence of intra-pump thrombosis (5). Thisobservation suggests that the left ventricle (LV) may be a relevant siteof local thrombosis and cardioembolism.

The normal LV flow pattern is characterized by a large diastolic vortexthat facilitates the transit of blood towards the aorta (9-11),contributing to diastolic transport and reducing kinetic energy lossesand cardiac work (12,13). Moreover, it allows for washing the LVcompletely in about 2 to 4 beats without inducing shear values highenough to activate platelets (14-16). Devices such as LVADs drasticallydisrupt the blood flow patterns in the heart and may lead to bloodstasis or abnormally large shear stresses (17,18).

The assessment of intraventricular flow patterns during LVAD treatmenthas been largely limited to in vitro (19, 20), in silico (21-23) and exvivo (24) models. These studies have suggested that pump speed, aorticvalve opening, cannula location and orientation may be importantdeterminants of intraventricular flow. However, modeling the flow insidethe LVAD-assisted ventricle is particularly challenging due to thecomplex interplays among the pulsatile function of the nativemyocardium, the continuous LVAD support, and the valves. Consequently,there is a need for in vivo data to quantitatively evaluateintraventricular flow, alterations in stasis and hemodynamic shear inLVAD-implanted patients.

A post-processing method to quantify LV blood stasis and cumulated shearwas previously implemented based on clinically applicableechocardiographic color-Doppler velocimetry (echo-CDV) (16, 25-27). Ananecdotal application of these methods to an LVAD-implanted patient hasbeen reported (18). Without wishing to be bound by theory, t ishypothesized that echo-CDV could be used to non-invasively characterizethe effect of LVAD support in LV hemodynamics and help understand theventricular-LVAD interplay. Therefore, the present study was designed tocharacterize the intraventricular flow patterns, as well as to quantifythe rates of blood wash-out and shear in the LV in a small sample ofpatients with Heartmate II LVADs. Flow patterns were compared with datafrom non-implanted subjects with either normal or dilated LVs. Finally,we assessed the effects of different LVAD pump speeds during ramp testson intraventricular flow.

Methods

Study Population

Seven subjects undergoing LVAD treatment were prospectively selectedfrom the Heart Failure Clinic at University of California San DiegoSulpizio Cardiovascular Center, in La Jolla, Calif. Inclusion criteriafor study participants were: 1) the presence of sinus rhythm; 2) asuitable apical ultrasonic window; 3) clinical stability enabling a rampstudy, 4) a Doppler signal-to-noise ratio that allowed reliablepostprocessing. All LVAD patients had ongoing treatment with a HeartMateII (Thoratec Corp., Pleasanton, Calif.) implanted between 2011-2017 andwere examined at a median of 16 (range 3-71) months after implantation.

Twenty normal subjects and twenty patients with non-ischemic dilatedcardiomyopathy (DCM) were used as controls. The studies were approved bythe corresponding Institutional Review Boards of the two institutions,and all participants provided written informed consent.

Image Acquisition and Analysis

Comprehensive 2-dimensional (2D) B-mode and color-Dopplerechocardiographic examinations were performed using Vivid 7 ultrasoundscanners and 2-4 MHz phase-array transducers (General ElectricHealthcare). Standard 3-chamber view color-Doppler sequences wereacquired at each patient's baseline—clinically determined optimal—pumpspeed, and at 200 rpm increments spanning the range: [baseline−400 rpm]to [baseline+400 rpm]. The total number of acquisitions in the sevenpatients was 32 (3 acquisitions were discarded due to poorsignal-to-noise ratio of the Doppler signal). EchoPac software (version110.1.2, General Electric Healthcare, Milwaukee, Wis.) was used todelineate the endocardial boundary from the apical long-axis B-modesequences and a board-certified cardiologist delineated the LVAD cannulaon the ventricle wall image using an ad-hoc graphical user interface inMATLAB (Mathworks). The echo-CDV algorithm was then used to calculatetime-resolved vector blood velocity maps in the LV, as previouslydescribed and validated in vitro (39) and in vivo (36). This algorithmwas modified to let blood flow through the cannula (18). Aorticinsufficiency (AI) was classified by a board-certified cardiologist andeach LVAD patient/speed case was grouped accordingly (absent/mild vs.moderate/severe).

From the reconstructed velocity field, the anteroseptal (clockwise, CW)and inferolateral (counter-clockwise, CCW) sections of the LV vortexring were identified (36, 40). For each vortex ring section (henceforthreferred to as vortex), the circulation, F (representing the swirlingstrength), the location along the LV normalized long axis, X (X=0corresponding to the base and X=1 to the apex), the radius, R (36), andthe ratio between circulation of the CW and CCW vortices were measured.These time-dependent quantities were averaged through the cardiac cycle.

To assess how the interplay between the native pulsatile cardiacfunction and the constant pump operation affects blood flow pulsatilityinside the ventricle, a velocity pulsatility map defined as V P(x,y)=T(|v(x, y, t_(max))|−|v(x, y, t_(min))|)/∫₀ ^(T)|v (x, y, t)|dt wascomputed, where T is the cardiac period and |v| is the absolute value ofthe velocity vector, which reaches its maximum and minimum values att_(max) and t_(min), respectively. Global chamber flow pulsatility wasquantified by the spatial average of VP, denoted as pulsatility indexVPI.

The time spent by blood inside the LV (residence time, T_(R) [s]) wascalculated by integrating in time a transport equation (18). In caseswith aortic regurgitation, the blood flowing back into the LV was alsomarked with T_(R)=0, allowing us to segment and track the regurgitantblood volume due to its sharp difference in T_(R) with respect to bloodalready present in the LV.

Shear-induced activation of platelets was modeled using a forcedadvection equation ∂_(t)Σ+∇(vΣ)=γ(x, y, t)^(a), where y(x, y, t) is ameasure of local instantaneous shear rate (50, 51). Based on thisequation, a cumulated shear index with dimensions of shear rate asCSI=Σ1/α−1 with α=2 was defined, based on empirical shear-inducedplatelet activation data (52). This family of models, with somevariations, have been previously used in computational fluid dynamicssimulations of shear-mediated hemolysis in LVAD pumps (53).

For the purpose of reporting and comparing data between groups,instantaneous T_(R) and CSI maps were obtained at the R-wave instantsubsequent to 5 seconds of integration (t=T_(5RW)). Blood domains withincreased residence time (T_(R)>2 s) were identified and their area(S_(R,2s)) on the imaging plane was computed as a percentage of the LVvolume (area in 2D). Likewise, domains with elevated exposure to shear(CSI>200 s⁻¹) were identified and their areas (S_(S,200/s)) computed.Global chamber indices of blood stasis and shear exposure werequantified by the spatial maxima and averages of T_(R) and CSI mapsacross the whole LV.

Statistical Analysis

Variables were reported as median and interquartile range. After testingfor the homogeneity of variance assumption (Levene's test), comparisonsamong groups were performed using Welch one-way ANOVA test followed byDunnett-Tukey-Kramer pairwise multiple comparison tests adjusted forunequal variances and sample sizes. Differences in flow indices in theramp study were analyzed using linear mixed-effects models accountingfor repeated measures and described by their fixed effect estimates (βcoefficient) and the ANOVA p-value of the model.

Results

The median age of the LVAD group was 74 (interquartile range 64-78)years old. All were males and six of them (86%) had non-ischemiccardiomyopathy. The median age of the DCM group was 62 (IQR 52-72) andall subjects were diagnosed with non-ischemic cardiomyopathy. Thehealthy control group had a median age of 56 (IQR 53-66). All subjectsin the DCM and healthy control groups were males to match LVAD group.Age-matching among groups was not performed due to the advanced age ofLVAD group. Echocardiographic and demographic data are reported in Table1.

TABLE 1 Demographic and echocardiographic data. LVAD ANOVA Pre-LVAD LVADDCM CONTROL p-value N 7 7 20 20 Age at examination 74 (62-76)   74(64-78) 62 (52-72) 56 (53-66) 0.292 Gender (males)  7 (100%) 20 (100%)20 (100%) Non-ischemic cardiomyopathy 6 (86%) 20 (100%) 0 (0%) Planneddestination therapy 3 (43%) — — Device type (HMII) —  7 (100%) — —Baseline pump speed (k.r.p.m.) —  9.0 (8.4-9.1) — — LV EDV (ml) 284(220-350) 104 (90-226) 129 (92-137) 75 (65-86) ^($) 0.0025 LV ESV (ml)240 (183-300)  77 (61-160)  89 (65-131) 27 (26-32) ^($) <0.001 LV EF 17(13-22)  28 (24-33) 28 (23-33) 63 (59-65) ^($, #) <0.001 HR 105(76-117)  68 (61-84) 61 (58-65) 69 (56-66) 0.233 HMII, EDV, ESV, EF andHR respectively stand for HeartMate II, end-diastolic volume,end-systolic volume, ejection fraction and heart rate. Data presented asmedian (IQR). ^($) p < 0.05 vs. LVAD group, ^(#) p < 0.05 beteen DCM andCONTROL groups.Blood Flow Patterns

FIG. 11A shows a sequence of instantaneous vector maps and magnitude ofLV blood velocity for representative subjects of the LVAD, DCM andnormal groups. Continuous suction from the LVAD cannula drives a strongmitral jet that extends all the way from the LV base to the apex andpersists throughout the whole cardiac cycle (FIG. 11A, left column). Bycomparison, in non-treated LVs the filling jet rolls up into a clockwiseswirling pattern that redirects blood towards the aortic valve duringlate diastole and early systole (FIG. 11A, center and right columns).

Quantification of vortex properties (FIG. 11B, Table 2) showed that themain CW vortex was significantly stronger in the LVAD and DCM groupsthan in the normal group with values of ΓCW=111 (76-148), 99 (73-133),and 60 (38-76) cm2/s, for the LVAD, DCM and normal groups, respectively(p=0.007). The main vortex was also larger and located closer to theapex in DCM and LVAD subjects than in normals [RCW=1.0 (0.9-1.5), 1(0.7-1.2) and 0.7 (0.5-0.8) cm, p=0.01, XCW=0.4 (0.4-0.4), 0.4 (0.3-0.5)and 0.3 (0.2-0.3), p<0.001]. Due to the more symmetric flow channelcreated by LVAD support, the secondary CCW vortex was stronger in LVADthan in DCM and normal groups [ΓCCW=43 (25-71), 14 (8-17) and 8 (5-16)cm2/s (p=0.05)].

LV blood flow in LVAD patients was less pulsatile over the cardiac cyclethan in the two control groups (FIG. 11D) with values of VPI=1.1(1.1-1.4), 2.5 (2.2-2.8) and 2.3 (2.1-2.7), p<0.001. Particularly, theirvelocity pulsatility maps (FIG. 11C) displayed a region of lowpulsatility that extended from the mitral valve to the pump cannula andco-localized with the jet induced by cannula suction. In contrast,pulsatility was higher and more uniformly distributed in DCM and normalsubjects.

TABLE 2 Flow properties in the three groups ANOVA LVAD DCM CONTROL Pvalue Vortex Circulation (cm2/s) CCW 43 (25-71)   14 (8-17) 8 (5-16)^(#) CW 111 (76-148)   99 (73-133) 60 (38-76) 0.007 Vortices CirculationRatio (cm2/s) CCW/CW 0.4 (0.3-0.6)  0.1 (0.1-0.2) 0.1 (0.1-0.3) 0.02Vortext Radius (cm) CCW 0.4 (0.3-0.8)  0.3 (0.2-0.4) 0.2 (0.1-0.3) CW  1(0.9-1.4) 1 (0.7-1.2) 0.7 (0.5-0.8) 0.01 Vortex Centroid Location (nd)CCW 0.3 (0.3-0.5)  0.3 (0.2-0.4) 0.3 (0.3-00.4) CW 0.4 (0.4-0.4)  0.4(0.3-00.5) 0.3 (0.2-0.3) ^($, #) <0.001 Pulsatility Index (nd) 1.1(1.1-1.4)  2.5 (2.2-2.8) ^($) 2.3 (2.1-2.7) ^($) <0.001 Residence Time(sec) Avg 0.4 (0.3-0.6)  1.9 (1.4-2.3) ^($) 1.4 (1.1-1.6) ^($) <0.001Max 2.2 (1.4-2.8)  5.2 (1.7-5.9) ^($) 5.4 (4.6-6.1) ^($) 0.001 Area ofregions with T_(R) > 2 sec (%) 0.1 (0-5.9)   40.7 (24.6-54.4) ^($) 27.1(18.1-31.4) 0.003 CSI (100/s) Avg 1.7 (0.9-1.8)  1.9 (1.5-2.3) 1.5(1.4-2.2) Max 6.4 (5-7)   6 (4.6-7.1) 5 (3.9-6.7) Area of regions withCSI > 200/s 27.5 (10.6-41.4) 37.6 (24-49.8) 32.9 (22.6-39.3) Datapresented as median (iqr). CCW: Counter clockwise, CW: Clockwise, T_(R):Residence Time, CSI: Cumulated shear index. ^($) p < 0.05 vs. LVADgroup, ^(#) p < 0.05 between DCM and CONTROL groups.Intraventricular Blood Transit and Shear Exposure

FIG. 12A displays instantaneous maps of residence time, TR(x, y), forthe same representative cases shown in FIG. 11. These maps suggest thatsuction from the cannula cleared the apical portion of the LV cavity inLVAD subjects. In contrast, non-implanted DCM patients showed largeregions of increased residence time that co-localized with thepersistent CW diastolic vortex typically found in these patients 15.Consistent with these results, the average LV residence time was lowestin the LVAD group [Average TR=0.4 (0.3-0.6) s, p<0.001], followed by theDCM [1.9 (1.4-2.3) s] and the normal [1.4 (1.1-1.6) s] groups (FIG. 12B& Table 2). Furthermore, LVAD patients had significantly smaller regionswith TR>2 seconds than DCM patients and normal controls [SR,2 s=0.1(0-5.9), 40.7 (24.6-54.4) and 27.1 (18.1-31.4) %, p=0.003].

Maps of cumulative shear index CSI(x, y, t) are shown in FIG. 13A. InLVAD patients, the basal-to-apical jet driven by cannula suction createdcontinuous shear exposure along the thin edges of the jet (see FIG.13A). This pattern led to cumulated shear in those regions and lowcumulative shear in the core of the jet (FIG. 13B). In non-LVAD theshear exposure had more complex dynamics: it was mostly localized at theedges of the E- and A-waves' filling jets and rolled up driven by themain clockwise LV vortex. Subsequently, the differences in LV washoutbetween the normal and the DCM patients transport had importantconsequences in terms of cumulated shear. While in normals most of theshear-exposed blood was ejected during systole, a substantial amount ofshear-exposed blood could remain trapped in the larger, more persistentvortex of the DCMs (compare central and right panels of FIG. 13A).Overall, LVAD patients had slightly higher maximum values of CSI[CSImax=6.4 (5-7), 6 (4.6-7.1) and 5 (3.9-6.7) s-1] (FIG. 13B & Table2). The IQRs in Table 2 suggest that the average value cumulative shearin the three groups should range between 90 and 230 s-1 and these datawas used to establish CSI>200 s-1 as a threshold for elevated cumulativeshear in our study. Based on this threshold, we found that the fractionof LV chamber size occupied by blood with elevated CSI was highest inthe DCM cohort and smallest in LVAD patients (FIG. 13C and Table 2).

The Effect of Aortic Insufficiency

The relatively wide spread of the data in the LVAD group (see FIGS. 12Band 13C) motivated a more detailed analysis of this group based onaortic insufficiency at baseline pump speed (i.e. AI cohort vs. no-AIcohort). FIG. 14A displays a sequence of maps of TR(x, y) spanning thecardiac cycle for a representative subject of the AI cohort. The plotsillustrate how a substantial volume of blood returns to the LV throughthe aortic valve forming a backflow jet that alternates with the fillingjet flowing through the mitral valve. The interaction between these twojets forces intraventricular blood to oscillate back and forth in thechamber, thus impairing LV washout and increasing residence time. Thisinteraction could be enhanced by LVAD support given that cannula suctiondrives the backflow blood region all the way to the LV apex, as shown inthe example case of FIG. 14A. In contrast, AI backflow is observed toremain confined near the LV base in non-implanted patients (data notshown).

Consistent with these observed changes in LV flow patterns, LVADpatients in the AI cohort showed an increase in LV blood averageresidence time (average TR=0.8 (0.6-1.3) s vs. 0.3 (0.2-0.3) s) and sizeof the region with TR>2 s (SR,2 s=11.1 (5.6-30.6)% vs. 0.1 (0.0-0.2)%)compared to the non-AI cohort. Note that these differences were notableeven if blood re-entering the LV from the aortic root was tagged withTR=0 seconds as boundary condition, an approximation that likelyunderestimates the true residence time in the AI cohort. The deficiencyin blood clearing observed in the AI cohort also caused shear-exposedblood to remain inside the LV for longer periods of time, allowing forlarger regions of elevated cumulative shear to form (e.g. compare theCSI(x, y) map of the AI case in FIG. 14B with the non-AI case of FIG.13B). Thus, the regions of elevated shear were found to occupy morespace the AI cohort than in the non-AI cohort with values of SS,200=42.6(41.4-50.5) % and 10.6 (7.2-15.8) %, even if the maximum values of CSIwere comparable for the two cohorts. See Table 3 for a summary ofresidence time and cumulative shear in the AI and non-AI cohorts.

TABLE 3 Residence time and cumulative shear indices for the LVADpatients split in two subsets according to the degree of aorticregurgitation. None-to-Low Moderate-to-Severe N 4 3 Residence Time (sec)Avg 0.3 (0.2-0.3) 0.8 (0.6-1.3) Max 1.6 (1.0-2.2) 3.4 (2.5-4.2) Size ofregions 0.1 (0.0-0.2) 11.1 (5.6-30.6) T_(R) > 2 sec (%) CSI (100/s) Avg0.9 (0.8-1.1) 2.0 (1.9-2.3) Max 5.6 (4.0-7.2) 6.4 (5.9-6.9) Size ofregions with 10.6 (7.2-15.8) 42.6 (41.4-50.5) CSI > 200/s Data presentedas median (iqr). T_(R): Residence Time, CSI: Cumulated shear indexSmall Variations of LVAD Speed Around Nominal Speed Scarcely Affect LVFlow Patterns

Blood flow velocity, pulsatility, residence time and cumulative shearwere mapped during ramp studies (FIG. 15) with small LVAD speed changes(each patient's baseline speed±400 rpm). These data suggest that,excepting flow pulsatility, the main features of intraventricular flowin LVAD patients remain almost constant with these pump speedvariations. Overall, with increased pump speed a more continuous directjet between the mitral valve and the LVAD cannula is established,leading to a decrease in pulsatility, but this does not significantlyimpact global indices of residence time or shear stresses.

Discussion

This Example has quantified how LVAD support affects intraventricularflow patterns, shear stresses and blood transport in a small cohort ofaxial flow LVAD patients compared to DCM patients and normal controls.Despite the increasingly widespread use of LVADs in advanced HF, thecharacterization of blood flow inside the LVAD-assisted ventricle hasnot been well studied and may provide important information to avoidcomplications after the surgery. These data reveal that, whilesubstantially altering the normal LV flow pattern, LVAD support largelyreverses the negative impact of DCM on blood transit through theventricle. LVAD patients were found to have values of intraventricularresidence time that are significantly lower than those of DCM patientsand even lower than normals. However, this reduction in residence timedid not correspond to a reduction in cumulative blood shear exposure.These data show that these results are relatively independent of LVADpump speed for small changes around the clinically indicated baselinevalue whereas blood transit worsened when LVAD support caused moderateor severe aortic insufficiency. These findings provide new insight intoblood flow dynamics in the LVAD-supported ventricle and may haveimportant implications for device programming and design.

Left ventricular flow patterns under LVAD support: The hemodynamics ofthe native LV are dominated by vortices that form during early fillingand atrial contraction and evolve into a large clockwise (CW) swirlingcell that follows the chiral arrangement of the LV inflow tract (LVIT),the main chamber and the aortic LV outflow tract (LVOT) (9, 10, 33).LVAD-treatment significantly affects these dynamics due to the suctionforces created by the pump (34, 35). These data show that LVAD treatmentre-routes the transit of blood through the LV so that it forms astraight channel between the LVIT and the LVAD cannula, instead offollowing a chiral path. The vorticity associated with the boundaries ofthe jet in LVAD-supported ventricles still results in a pair ofvortices. However, consistent with existing in vitro data (19), the netCW rotational motion of blood found in the native LV is reduced by LVADtreatment by stronger counter-CW vortices.

In cases with aortic insufficiency, backflow from the aortic tractformed a counter-CW swirling blood “compartment” that interacted withthe natural CW swirling region, creating two separate pockets of bloodthat rotate inside the LV in alternating directions, and affecting bloodresidence time and its exposure to shear. Suction from the cannula mayaccentuate the effects of AI in LVAD patients by driving the aorticbackflow close to the LV apex.

The efficiency of re-routing blood transit through the LV: While thenative ventricle alternates between reservoir (diastole) and booster(systole) function, LVAD-support forces the ventricle to operate as aconduit. The potential implications of blood re-routing in the totalwork exerted by the native heart remain debatable after two decades ofinvestigation (10, 13, 14, 33, 36). The implications for plateletactivation and thrombosis, which are particularly relevant in LVADpatients, have received less attention. Simulation studies in idealizedchamber geometries (13) have shown that the chiral arrangement of theLVIT, the main LV chamber and the LVOT minimize the shear between thefilling jet and the intraventricular blood. In contrast, we found thatLVAD patients experienced more exposure to shear in the thin layerssurrounding the inflow jets than DCM patients and normals.

Flow measurements in LVAD and normal subjects described here suggestthat, by establishing a shorter, straighter route for blood transitinside the ventricle, LVAD treatment significantly decreases the LVresidence time of blood, but the same trend did not apply to cumulativeexposure to shear. It was found that strong persistent vortices in DCMpatients can trap blood inside the LV for long times, during which bloodis continuously exposed to shear. LVAD treatment causes highinstantaneous shear stresses along the edges of the longitudinal jetcreated by suction at the cannula. However, by improving LV bloodtransit, it prevents blood from being exposed to increased shear forprolonged periods. When LVAD suction was strong enough to trigger aorticinsufficiency the re-routing of blood transit by LVAD treatment wasdisturbed, becoming less efficient in balancing residence time withblood exposure to shear. These results highlight the need of consideringthe efficiency of re-routing LV blood transit by jointly assessing bloodstasis and cumulative shear as they are tightly interrelated, but do notnecessarily vary in the same direction after an intervention. Theseconsiderations may be particularly useful for determining the idealposition and angle of the LVAD cannula, which have been suggested toaffect LV blood transit (20-23).

Other considerations: The development of in silico and in vitro analysesof intraventricular flow in the LVAD-supported ventricle (19, 21-24) hasnot been paralleled by a similar surge in pre-clinical or clinicalexperiments. This lag may in part be due to the inability of performingMRI on LVAD patients. In the current study, the utility of measuringintraventricular flows with ultrasound has been demonstrated. Moreover,it is expected that these new in vivo analyses will facilitate furtherwork to overcome limitations of in vitro and in silico models such asthe difficulty of modeling myocardial contraction, relaxation, torsion,valves dynamics, and the physiological response to changes in LVADsupport.

The noninvasiveness, portability and device compatibility ofechocardiography make this modality well suited for the assessment ofintraventricular flow in LVAD patients. In the last decade, severalechocardiographic methods have been developed to visualize and quantifyblood flow in the left ventricle (37). Particle-image velocimetryapplied to contrast ultrasound sequences (echo-PIV) has proven usefuland, given that use of contrast agents seems to be safe in patientsimplanted with third-generation LVADs (38), it is a promising modalityto quantify LV flow in these patients. However, this technique requiresfine-tuning of the contrast agent infusion (39), which may beparticularly challenging in LVAD patients whose pumps destroy contrastagent bubbles (40).

When used in the LV apical long-axis view, echocardiographiccolor-Doppler velocimetry has good agreement with in silico (41), invitro (25) and in vivo reference methods (28). Because it imposes freeslip boundary conditions at the LV endocardium, it is possible thatecho-CDV underestimates endocardial blood shear. Nevertheless, thecumulative shear values obtained here are in good agreement with valuesmeasured in vitro with PIV (31).

The LVAD cohort in this pilot study is small and heterogeneous, althoughmost patients had non-ischemic cardiomyopathy (86%) and were >50 yearsof age (86%). Considering this, the DCM cohort was included as anattempt to control for age and non-ischemic cardiomyopathy.

Clinical implications: LVAD therapy is associated with“hemocompatibility events” such as cerebrovascular accidents, pumpthrombosis and hemolysis potentially related to thrombosis inside theventricle. These complications occur in similar rates in both axial andcentrifugal pumps. Currently, there is a lack of clinical tools to guideoptimal LVAD settings and cannula placement. Echocardiographic rampstudies are sometimes used to choose pump speeds, but there is limiteddata showing their utility and no evidence these decrease rates ofthromboembolic events. Thrombosis is associated with platelet activationand relative stasis, hemolysis is known to be associated with high shearstress, but currently the risks of these are difficult to estimate inclinical practice and therefore difficult to mitigate. The present datahave demonstrated the utility of echo-CDV to evaluate LV hemodynamics inpatients with LVADs, and to quantify both LV stasis and shear exposure,which are associated with platelet activation. It was observed that LVstasis was reduced in the group with LVADs compared to the DCM group,while shear was not and pump settings that result in significant aorticinsufficiency were associated with a relative increase in stasis andshear exposure. Though AI is a relatively frequent complication of LVADuse (42), an association between AI and thromboembolic events has notbeen established. Nonetheless, this suggests a potential connectionbetween these two phenomena. In addition, echo-CDV is expected to beuseful in guiding LVAD cannula placement and optimal pump settings andtherefore decrease the rate of complications and improve outcomes.

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OTHER EMBODIMENTS

It is to be understood that while the invention has been described inconjunction with the detailed description thereof, the foregoingdescription is intended to illustrate and not limit the scope of theinvention, which is defined by the scope of the appended claims. Otheraspects, advantages, and modifications are within the scope of thefollowing claims. Indeed, various modifications of the invention inaddition to those described herein will become apparent to those skilledin the art from the foregoing description and the accompanying figures.Such modifications are intended to fall within the scope of the appendedclaims It is further to be understood that all values are approximate,and are provided for description. Patents, patent applications,publications, product descriptions, and protocols are cited throughoutthis application, the disclosures of which are incorporated herein byreference in their entireties for all purposes.

What is claimed is:
 1. A method for identifying a region of hemolysisinside a cardiac chamber or blood vessel of a subject having a leftventricular assist device (LVAD) comprising: obtaining flow-velocityimages of blood inside the cardiac chamber or the blood vessel of thesubject; calculating hemolysis using the flow-velocity images using thefollowing equation:$\frac{\Delta\;{PfHb}}{Hb} = {C\;\Sigma^{a}T_{R}^{b - 1}}$ wherein PfHbis plasma free hemoglobin, Hb is total hemoglobin in the blood, Σ iscumulative fluid shear stress experienced by blood particles inseconds-1, TR is residence time of the blood particles in seconds, anda, b, and c are empirical constants; wherein Σ is determined using theforced transport equation:${\frac{D\;\Sigma}{Dt} = {{{\partial_{t}\Sigma} + {\nabla{\cdot \left( {v\;\Sigma} \right)}}} = S}},{{\Sigma\left( {x,{t = 0}} \right)} = 0},{{\Sigma\left( {x_{inlet},t} \right)} = 0},$wherein S is the Von-Mises stress at each point of space and time insidea left ventricle, and wherein S is determined from a velocity fieldobtained from the flow velocity images.
 2. The method of claim 1,further comprising: generating numerical metrics of blood flow,comprising: calculating one or more of residence time (TR), standarddeviation of residence time (σTR), inside the cardiac chamber or theblood vessel using the flow-velocity images to generate the numericalmetrics of the blood flow; and calculating one or more of cumulativevon-Mises stress map (Σ), standard deviation of residence von-Misesstress (σΣ), inside the cardiac chamber or the blood vessel using theflow velocity images to generate the numerical metrics of the bloodflow; or combinations thereof; and using the numerical metrics toidentify and characterize the region of hemolysis.
 3. The method ofclaim 2, wherein generating the numerical metrics of the blood flowcomprises calculating the plasma free hemoglobin (PfHb) inside thecardiac chamber or the blood vessel, and the standard deviation ofplasma free hemoglobin (σPfHb).
 4. The method of claim 2, comprisingcalculating the standard deviation of plasma free hemoglobin (σPfHb) inone or more regions inside the cardiac chamber or the blood vessel. 5.The method of claim 2, wherein generating the numerical metrics of theblood flow comprises calculating the rate of distortion of blood flowinside any cardiac chamber or blood vessel.
 6. The method of claim 5,comprising calculating the blood flow's rate of distortion in one ormore regions inside the cardiac chamber or the blood vessel.
 7. Themethod of claim 2, wherein generating the numerical metrics of the bloodflow comprises calculating a size, shape, mobility, distance to achamber wall, and perimeter in contact with the chamber wall of one ormore regions inside the cardiac chamber or the blood vessel.
 8. Themethod of claim 2, wherein the cardiac chamber is any cardiac chamber orblood vessel in which blood velocity can be resolved.
 9. The method ofclaim 2, wherein the cardiac chamber is a left ventricular chamber, leftatrium chamber, left atrial appendage, right-ventricular chamber, orright atrium chamber.
 10. The method of claim 2, wherein theflow-velocity images comprise one, two, or three-dimensional imagesresolved in time.
 11. The method of claim 2, wherein multipleflow-velocity images are obtained using different velocity scales, andwherein data from the obtained flow velocity images are retrospectivelymerged to generate a flow map, a residence time (TR) map, a cumulativevon-Mises stress map (Σ), a rate of distortion map, or combinationsthereof.
 12. The method of claim 2, wherein calculating the residencetime (T_(R)) of blood particles comprises utilizing the equation:${\frac{\partial T_{R}}{\partial t} + {\nabla{\cdot \left( {\overset{\rightarrow}{v}\; T_{R}} \right)}}} = 1.$13. The method of claim 2, wherein the standard deviation of Σ is causedby noise in velocity measurements in the flow-velocity images, andwherein calculating the standard deviation of Σ comprises utilizing theequation:σ_(Σ)(x,t)=√{square root over (S _(Σ)(x,t)−Σ²(x,t))} wherein SΣ and Σobey the equations:${\frac{\partial\Sigma}{\partial t} + {\nabla{\cdot \left( {\overset{\rightarrow}{v}\Sigma} \right)}}} = {S + {\nabla{\cdot \left( {k{\nabla\Sigma}} \right)}}}$${{\frac{\partial S_{\Sigma}}{\partial t} + {\nabla{\cdot \left( {\overset{\rightarrow}{v}S_{\Sigma}} \right)}}} = {{2\;\Sigma} + {\nabla{\cdot \left( {k{\nabla S_{\Sigma}}} \right)}}}},$and wherein diffusivity coefficient k represents uncertainty introducedby the noise in the velocity measurements.
 14. The method of claim 2,wherein the standard deviation of TR is caused by noise in velocitymeasurements in the flow-velocity images, and wherein calculating thestandard deviation of TR comprises utilizing the equation:σ_(TR)(x,t)=√{square root over (S _(R)(x,t)−T _(R) ²(x,t))} whereinS_(R) and T_(R) obey the equations:${\frac{\partial T_{R}}{\partial t} + {\nabla{\cdot \left( {\overset{\rightarrow}{v}T_{R}} \right)}}} = {1 + {\nabla{\cdot \left( {k{\nabla T_{R}}} \right)}}}$${{\frac{\partial S_{R}}{\partial t} + {\nabla{\cdot \left( {\overset{\rightarrow}{v}S_{R}} \right)}}} = {{2T_{R}} + {\nabla{\cdot \left( {k{\nabla S_{R}}} \right)}}}},$and wherein diffusivity coefficient k represents uncertainty introducedby the noise in the velocity measurements.
 15. The method of claim 2,wherein a distribution of values of cumulative von-Mises stress at eachinstant of time and each point in space, which distribution of values ofcumulative von-Mises stress is caused by noise in velocity measurementsin the flow-velocity images, wherein a probability density function ofdistribution p(Σ, x, t) is calculated utilizing the equation:${\frac{\partial p}{\partial t} = {{- \frac{\partial({vp})}{\partial x}} - \frac{\partial p}{\partial T} + {\frac{\partial}{\partial x}\left( {k\frac{\partial p}{\partial x}} \right)}}},$and wherein diffusivity coefficient k represents uncertainty introducedby the noise in the velocity measurements.
 16. The method of claim 2,wherein a distribution of values of residence time emerges at eachinstant of time and each point in space, which distribution of values ofresidence time is caused by noise in velocity measurements in theflow-velocity images, wherein a probability density function ofdistribution p(T,x,t) is calculated utilizing the equation:${\frac{\partial p}{\partial t} = {{- \frac{\partial({vp})}{\partial x}} - \frac{\partial({Sp})}{\partial S} + {\frac{\partial}{\partial x}\left( {k\frac{\partial p}{\partial x}} \right)}}},$and wherein diffusivity coefficient k represents uncertainty introducedby the noise in the velocity measurements.
 17. The method of claim 2,wherein the numerical metrics of the blood flow are used to identifysize, location, or both, of one or more regions within the cardiacchamber or the blood vessel.
 18. The method of claim 1, whereinobtaining the flow-velocity images of the blood inside the cardiacchamber or the blood vessel is performed using a medical image basedapparatus able to determine blood flow velocity field.
 19. The method ofclaim 18, wherein the medical image-based apparatus is an echocardiogramapparatus, a magnetic resonance imaging (MRI) apparatus, anechocardiographic imaging apparatus, a 2D color-Doppler velocimetry(echo-CDV) apparatus, an echo-PIV apparatus, a synthetic apertureultrasound apparatus, or a transverse oscillation ultrasound vectorvelocimetry apparatus.
 20. A method for evaluating an intraventricularregion of hemolysis inside a cardiac chamber or blood vessel of a firstsubject comprising: implanting a left ventricular assist device (LVAD)into the first subject at a first location, wherein the LVAD operatesunder a first set of operating parameters; obtaining flow-velocityimages of blood inside the cardiac chamber or the blood vessel of thefirst subject; calculating hemolysis using the flow-velocity imagesusing the following equation:$\frac{\Delta\;{PfHb}}{Hb} = {C\;\Sigma^{a}T_{R}^{b - 1}}$ wherein PfHbis plasma free hemoglobin, Hb is total hemoglobin in the blood, Σ iscumulative fluid shear stress experienced by blood particles inseconds-1, TR is residence time of the blood particles in seconds, anda, b, and c are empirical constants; wherein Σ is determined using theforced transport equation:${\frac{D\;\Sigma}{Dt} = {{{\partial_{t}\Sigma} + {\nabla{\cdot \left( {v\;\Sigma} \right)}}} = S}},{{\Sigma\left( {x,{t = 0}} \right)} = 0},{{\Sigma\left( {x_{inlet},t} \right)} = 0},$wherein S is the Von-Mises stress at each point of space and time insidea left ventricle, and wherein S is determined from a velocity fieldobtained from the flow-velocity images.
 21. The method of claim 20,wherein the LVAD is surgically implanted into the first subject.
 22. Themethod of claim 20, wherein the LVAD is temporarily implanted into thefirst subject.
 23. The method of claim 22, wherein the LVAD is acatheter-based LVAD.
 24. The method of claim 20, wherein the cardiacchamber is a left ventricular chamber.
 25. The method of claim 20,further comprising evaluating an intraventricular region of hemolysisinside a cardiac chamber or blood vessel of a second subject comprising:implanting a LVAD into the second subject at a second location, whereinthe LVAD operates under a second set of operating parameters;calculating hemolysis using the flow-velocity images using the followingequation: $\frac{\Delta\;{PfHb}}{Hb} = {C\;\Sigma^{a}T_{R}^{b - 1}}$wherein PfHb is the plasma free hemoglobin, Hb is the total hemoglobinin the blood (intracellular and extracellular), Σ is the cumulativefluid shear stress experienced by blood particles in seconds-1, TR isthe residence time of the blood particles in seconds, and a, b, and care empirical constants; wherein Σ is determined using the forcedtransport equation:${\frac{D\;\Sigma}{Dt} = {{{\partial_{t}\Sigma} + {\nabla{\cdot \left( {v\;\Sigma} \right)}}} = S}},{{\Sigma\left( {x,{t = 0}} \right)} = 0},{{\Sigma\left( {x_{inlet},t} \right)} = 0},$wherein S is the Von-Mises stress at each point of space and time insidethe left ventricle, and wherein S is determined from a velocity fieldobtained from the flow-velocity images.
 26. The method of claim 25,wherein the first location, the second location, or both is the locationof cannula placement.
 27. The method of claim 25, wherein the first setof operating parameters, the second set of operating parameters, or bothincludes pump speed.
 28. The method of claim 25, wherein the cardiacchamber of the second subject is a left ventricular chamber.
 29. Themethod of claim 20, wherein the first subject or the second subject is amammal.
 30. The method of claim 29, wherein the mammal is a human. 31.The method of claim 29, wherein the mammal is selected from the groupconsisting of: a monkey, a dog, a cat, a cow, a horse, a pig, a rat, anda mouse.